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Nanotechnology's impact on semiconductor industry advancement, particularly through the engineering of nanostructures like nanowires, opens new possibilities for material functionality due to the tunable physical properties of nanostructures compared to bulk materials. This paper presents a comprehensive study on group IV semiconductors and their binaries across four polytypes: 2H, 3C, 4H, and 6H, focusing on their optoelectronic application potential. Deep understanding of these polytypes is particularly relevant for nanowire-based technologies. Through first principles modeling, we examine the structural and electronic properties of these materials, emphasizing their band structure, stability, and the feasibility for light-emitting applications. We use a generalized Ising model to discuss materials stability and tendency for polytypism. We also determine relative band edge positions and employ a six-band k⋅p model for a detailed understanding of the materials' electronic properties. Due to the comprehensive nature of this study, we provide insight on the chemical trends present in all of the studied properties. Our theoretical predictions align well with the existing experimental data, suggesting new avenues for nanostructure-based device development. The discussion extends to the implications of these findings for the fabrication of optoelectronic devices with the studied IV–IV materials, highlighting the challenges and opportunities for future research in nanowire synthesis and their applications. [ABSTRACT FROM AUTHOR]

The accuracy of density-functional theory (DFT) calculations is ultimately determined by the quality of the underlying approximate functionals, namely the exchange-correlation functional in electronic DFT and the excess functional in the classical DFT formalism of fluids. For both electrons and fluids, the exact functional is highly nonlocal, yet most calculations employ approximate functionals that are semi-local or nonlocal in a limited weighted-density form. Machine-learned (ML) nonlocal density-functional approximations show promise in advancing applications of both electronic and classical DFTs, but so far these two distinct research areas have implemented disparate approaches with limited generality. Here, we formulate a universal ML framework and training protocol to learn nonlocal functionals that combine features of equivariant convolutional neural networks and the weighted-density approximation. We prototype this new approach for several 1D and quasi-1D problems and demonstrate that functionals with exactly the same hyperparameters achieve excellent accuracy for a diverse set of systems, including the hard-rod fluid, the inhomogeneous Ising model, the exact exchange energy of electrons, the electron kinetic energy for orbital-free DFT, as well as for liquid water with 1D inhomogeneities. These results lay the foundation for a universal ML approach to approximate exact 3D functionals spanning electronic and classical DFTs. [ABSTRACT FROM AUTHOR]

ModelHamiltonian is a free, open source, and cross-platform Python library designed to express model Hamiltonians, including spin-based Hamiltonians (Heisenberg and Ising models) and occupation-based Hamiltonians (Pariser–Parr–Pople, Hubbard, and Hückel models) in terms of 1- and 2-electron integrals, so that these systems can be easily treated by traditional quantum chemistry software programs. ModelHamiltonian was originally intended to facilitate the testing of new electronic structure methods using HORTON but emerged as a stand-alone research tool that we recognize has wide utility, even in an educational context. ModelHamiltonian is written in Python and adheres to modern principles of software development, including comprehensive documentation, extensive testing, continuous integration/delivery protocols, and package management. While we anticipate that most users will use ModelHamiltonian as a Python library, we include a graphical user interface so that models can be built without programming, based on connectivity/parameters inferred from, for example, a SMILES string. We also include an interface to ChatGPT so that users can specify a Hamiltonian in plain language (without learning ModelHamiltonian's vocabulary and syntax). This article marks the official release of the ModelHamiltonian library, showcasing its functionality and scope. [ABSTRACT FROM AUTHOR]

This study explores the effect of molecular permanent dipole moment (PDM) on aggregation of guest molecules in phosphorescent host–guest organic light-emitting diodes (OLEDs). Through a combination of photoluminescence measurements, high-angle annular dark-field scanning transmission electron microscopy analysis, and an Ising model based physical vapor-deposition simulation, we show that higher PDM of tris[2-phenylpyridinato-C2,N]iridium(III) guest can actually lead to a reduced aggregation relative to tris[bis[2-(2-pyridinyl-N)phenyl-C] (acetylacetonato)iridium(III) when doped into a non-polar host 1,3,5-tris(carbazol-9-yl)benzene. This study further explores the effect of host polarity by using a polar host 3′,5′-di(carbazol-9-yl)-[1,1′-biphenyl]-3,5-dicarbonitrile, and it is shown that the polar host leads to reduced guest aggregation. This study provides a comprehensive understanding of the impact of molecular PDM on OLED material efficiency and stability, providing insights for optimizing phosphorescent OLED materials. [ABSTRACT FROM AUTHOR]

The stability of a mixture of two different surface reconstructions is investigated focusing on GaN(0001) surface mixed with Ga a d (2 × 2) and 3Ga-H(2 × 2) domains using the density functional theory calculations. Since the number of candidate structures is enormous, the structures sampled by Bayesian optimization are analyzed. As a result, the local electron counting (EC) rule alone was found to be insufficient to explain such stability. Then, augmenting the EC rule, a data-driven Ising model is proposed. The model allows the evaluation of the whole enormous number of candidate structures. The approach is expected to be useful for theoretical studies of such mixtures on various semiconductor surfaces. [ABSTRACT FROM AUTHOR]

The Ising model, initially proposed about 100 years ago to explain ferromagnetism and phase transitions, has become a central pillar of statistical physics and a powerful tool for diverse applications in other fields including environmental studies. In this paper, we introduce continuous spin values between −1 and +1 to a two-dimensional Ising model and utilize the generalized Ising lattice to simulate the dynamics of sea ice/water transition for a large area of 1500 km by 1500 km in the Arctic region. The simulation process follows the Metropolis-Hastings algorithm and incorporates an innovative factor to account for the inertia of spin value changes. Using the sea ice concentration data collected by the National Snow and Ice Data Center, our results exhibit striking similarity between the simulated and the observed ice melting and freezing dynamics, and two numerical measures from the simulation—the ice coverage percentage and the ice extent—match closely with the data statistics. Moreover, the model's best-fit parameters demonstrate the substantial impact of the external forces, which can be further enriched and linked to the environmental factors in other climate change research. [ABSTRACT FROM AUTHOR]

In this work, we perform a density matrix renormalization group study of chains of planar rotors interacting via dipolar interactions. By exploring the ground state from weakly to strongly interacting rotors, we find the occurrence of a quantum phase transition between a disordered and a dipole-ordered quantum state. We show that the nature of the ordered state changes from ferroelectric to antiferroelectric when the relative orientation of the rotor planes varies and that this change requires no modification of the overall symmetry. The observed quantum phase transitions are characterized by critical exponents and central charges, which reveal different universality classes ranging from that of the (1 + 1)D Ising model to the 2D classical XY model. [ABSTRACT FROM AUTHOR]

We investigate the nucleation dynamics of the three-dimensional random field Ising model under an external field. We use umbrella sampling to compute the free-energy cost of a critical nucleus and use forward flux sampling for the direct estimation of nucleation rates. For moderate to strong disorder, our results indicate that the size of the nucleating cluster is not a good reaction coordinate, contrary to the pure Ising model. We rectify this problem by introducing a coordinate that also accounts for the location of the nucleus. Using the free energy barrier to predict the nucleation rate, we find reasonable agreement, although deviations become stronger as disorder increases. We attribute this effect to cluster shape fluctuations. We also discuss finite-size effects on the nucleation rate. [ABSTRACT FROM AUTHOR]

The partition function of the Ising model of a graph \(G=(V,E)\) is defined as \(Z_{\operatorname{Ising}}(G;b)=\sum_{\sigma:V\to \{0,1\}} b^{m(\sigma)}\), where \(m(\sigma)\) denotes the number of edges \(e=\{u,v\}\) such that \(\sigma(u)=\sigma(v)\). We show that for any positive integer \(\Delta\) and any graph \(G\) of maximum degree at most \(\Delta\), \(Z_{\operatorname{Ising}}(G;b)\neq 0\) for all \(b\in \mathbb{C}\) satisfying \(|\frac{b-1}{b+1}| \leq \frac{1-o_\Delta(1)}{\Delta-1}\) (where \(o_\Delta(1) \to 0\) as \(\Delta\to \infty\)). This is optimal in the sense that \(\tfrac{1-o_\Delta(1)}{\Delta-1}\) cannot be replaced by \(\tfrac{c}{\Delta-1}\) for any constant \(c › 1\) subject to a complexity theoretic assumption.To prove our result we use a standard reformulation of the partition function of the Ising model as the generating function of even sets. We establish a zero-free disk for this generating function inspired by techniques from statistical physics on partition functions of polymer models. Our approach is quite general and we discuss extensions of it to certain types of polymer models.Mathematics Subject Classifications: 05C31, 82B20, 68W25Keywords: Ising model, partition function, even set, polymer model, Fisher zeros, approximate counting

AbstractA composite likelihood is an inference function derived by multiplying a set of likelihood components. This approach provides a flexible framework for drawing inferences when the likelihood function of a statistical model is computationally intractable. While composite likelihood has computational advantages, it can still be demanding when dealing with numerous likelihood components and a large sample size. This paper tackles this challenge by employing an approximation of the conventional composite likelihood estimator based on a stochastic optimization procedure. This novel estimator is shown to be asymptotically normally distributed around the true parameter. In particular, based on the relative divergent rate of the sample size and the number of iterations of the optimization, the variance of the limiting distribution is shown to compound for two sources of uncertainty: the sampling variability of the data and the optimization noise, with the latter depending on the sampling distribution used to construct the stochastic gradients. The advantages of the proposed framework are illustrated through simulation studies on two working examples: an Ising model for binary data and a gamma frailty model for count data. Finally, a real-data application is presented, showing its effectiveness in a large-scale mental health survey. [ABSTRACT FROM AUTHOR]

Community detection in multi-layer networks, which aims at finding groups of nodes with similar connective patterns among all layers, has attracted tremendous interests in multi-layer network analysis. Most existing methods are extended from those for single-layer networks, which assume that different layers are independent. In this article, we propose a novel community detection method in multi-layer networks with inter-layer dependence, which integrates the stochastic block model (SBM) and the Ising model. The community structure is modeled by the SBM model and the inter-layer dependence is incorporated via the Ising model. An efficient alternative updating algorithm is developed to tackle the resultant optimization task. Moreover, the asymptotic consistencies of the proposed method in terms of both parameter estimation and community detection are established, which are supported by extensive simulated examples and a real example on a multi-layer malaria parasite gene network. for this article are available online. [ABSTRACT FROM AUTHOR]

We discuss non-equilibrium thermodynamics of the mean-field Ising model from a geometric perspective, focusing on the thermodynamic limit. When the number of spins is finite, the Gibbs equilibria form a smooth Legendrian submanifold in the thermodynamic phase space whose points describe the stable macroscopic states of the system. We describe the convergence of these smooth Legendrian submanifolds, as the number of spins goes to infinity, to a singular Legendrian submanifold, admitting an analytic continuation that contains both the stable and metastable states. We also discuss the relaxation to a Gibbs equilibrium when the physical parameters are changed abruptly. The relaxation is defined via the gradient flow of the free energy with respect to the Wasserstein metric on microscopic states, that is, in the geometric language, via the gradient flow of the generating function of the equilibrium Legendrian with respect to the ghost variables. This leads to a discrete Fokker-Planck equation when the number of spins is finite. We show that in the thermodynamic limit this description is closely related to the seminal model of relaxation proposed by Glauber. Finally, we find a special range of parameters where such relaxation happens instantaneously, along the Reeb chords connecting the initial and the terminal Legendrian submanifolds. [ABSTRACT FROM AUTHOR]

We consider the continuum version of the random field Ising model in one dimension: this model arises naturally as weak disorder scaling limit of the original Ising model. Like for the Ising model, a spin configuration is conveniently described as a sequence of spin domains with alternating signs (domain-wall structure). We show that for fixed centered external field and as spin-spin couplings become large, the domain-wall structure scales to a disorder dependent limit that coincides with the infinite disorder fixed point process introduced by D. S. Fisher in the context of zero temperature quantum Ising chains. In particular, our results establish a number of predictions that one can find in Fisher et al. (Phys Rev E 64:41, 2001). The infinite disorder fixed point process for centered external field is equivalently described in terms of the process of suitably selected extrema of a Brownian trajectory introduced and studied by Neveu and Pitman (in: Séminaire de probabilités XXIII. Lecture notes in mathematics, vol 1372, pp 239–247, 1989). This characterization of the infinite disorder fixed point is one of the important ingredients of our analysis. [ABSTRACT FROM AUTHOR]

We attempt to study the mixed-spin Ising on two decorated ferrimagnetic ternary metallic nanoislands possessing hexagonal and square structures, with a mixture of spin numbers 3/2, 1, and 1/2. Via the finite cluster approximation, the critical and compensation characteristics have been explored by implementing the influences of decorating and interface exchange couplings ( J 1 , J 2 ), along with the crystal fields ( D σ , D S ) on the phase diagrams and magnetizations. In the absence of crystal fields, the hexagonal structure exhibits only the second-order transition with one or two compensation points; meanwhile, the square structure undergoes the multiple transitions behavior (two or three transition temperatures) with a first-order transition at low temperatures. The inclusion of the crystal fields demonstrates the elevation of the ferrimagnetic region of order. Interestingly, we have uncovered under only the effect of D S acting on spin-1 sublattice the occurrence of the first-order with reentrance indicating two and three transitions for the hexagonal and square structures, respectively. Finally, under a uniform crystal field ( D σ = D S = D), the first-order keeps existing only for the square nanoisland. [ABSTRACT FROM AUTHOR]

The molecular approach of a spin model is constructed on the Bethe lattice (BL), and then it is examined in terms of exact recursion relations. Rather than assuming that each BL site is inhabited by a single spin, each site is occupied by two spin-1/2 atoms A and B, forming a molecule. Each molecule is considered to contain two spin-1/2 atoms, as well as q = 3 , 4 , or 6 nearest-neighbor molecules. In addition to the internal interactions between the atoms of each molecule, the molecules interact via their atoms in terms of bilinear interaction parameters J. Atoms of a molecule interact with J A i B i , while the molecules interact via their atoms in terms of J A i B i + 1 = J B i A i + 1 and J A i A i + 1 = J B i B i + 1 . After obtaining the magnetizations of each atom in the central molecule of the BL, the average magnetization of the molecule is determined. It is found that the model presents first-and second-order and random phase transitions. The model also displays tricritical, bicritical and end points, in addition to reentrant behavior for appropriate J values. [ABSTRACT FROM AUTHOR]

The Ising model has become a popular psychometric model for analyzing item response data. The statistical inference of the Ising model is typically carried out via a pseudo-likelihood, as the standard likelihood approach suffers from a high computational cost when there are many variables (i.e., items). Unfortunately, the presence of missing values can hinder the use of pseudo-likelihood, and a listwise deletion approach for missing data treatment may introduce a substantial bias into the estimation and sometimes yield misleading interpretations. This paper proposes a conditional Bayesian framework for Ising network analysis with missing data, which integrates a pseudo-likelihood approach with iterative data imputation. An asymptotic theory is established for the method. Furthermore, a computationally efficient Pólya–Gamma data augmentation procedure is proposed to streamline the sampling of model parameters. The method's performance is shown through simulations and a real-world application to data on major depressive and generalized anxiety disorders from the National Epidemiological Survey on Alcohol and Related Conditions (NESARC). [ABSTRACT FROM AUTHOR]

We have investigated the effect of potassium (K) doping at Sr-sites on the structural, magnetic, magnetocaloric, and critical behaviors of La0.65Sr0.35−xKxMnO3(x = 0.075 and 0.15) perovskite manganite. These samples were successfully prepared using the sol–gel method. X-ray powder diffraction (XRD) showed that our samples crystallize in the rhombohedral structure within space group R 3 ¯ c (No.167). As the temperature increases, the synthesized compounds undergo a phase transition from ferromagnetic (FM) to paramagnetic (PM) material. The magnetocaloric effect has been evaluated by assessing the isothermal magnetization curve at different temperatures close to the Curie temperature (TC), employing the Maxwell relationship. At an applied field with a magnitude of 5 T, the maximum magnetic entropy change ( - Δ S M max) and relative cooling power (RCP) are 4.25 J/kg K and 288 J/kg for x = 0.075 and 3.67 J/kg K and 267 J/kg for x = 0.15, respectively. The important magnetic entropy change, along with the adaptable Curie temperature and high relative cooling power (CP), renders these oxides beneficial for magnetic refrigeration across extensive temperature ranges, including near-room temperatures. Critical phenomena have been studied using different theoretical models: modified Arrott plots (MAP), Kouvel–Fisher (KF) method and critical isotherm (CI) analysis. The obtained critical exponents (β, γ and δ) revealed that the simple x = 0.075 is consistent with the 3D Ising model, whereas the critical exponents determined for x = 0.15 were close to the 3D Heisenberg model. The obtained values of the critical exponents were verified by the Widom relationship and scaling hypothesis, which confirmed the associated models. [ABSTRACT FROM AUTHOR]

ABSTRACT Complex system models of attitudes, such as the Hierarchical Ising Opinion Model (HIOM), suggest that a person's involvement in an attitude object could be linked to attitude extremity and polarization. Despite its potential to integrate various theories of attitude change and despite the implications it could hold for attitude research, this assumption has not yet been studied systematically. We investigate the role of involvement in five large‐scale, representative surveys on general political orientation and attitudes towards the EU and COVID‐19 vaccines, conducted in 79 different countries over the last 8 years. We propose criteria to classify the degree of ideological divergence and introduce a modality detection measure suited for ordinal data and large sample sizes. We find that involvement is linked to attitude extremity and that predictions of HIOM are validated in a topic‐specific dataset on COVID‐19 vaccines. Results on political orientation and general attitudes towards the EU show either no effect of involvement or patterns that contradict HIOM's predictions. We discuss implications for the measurement of involvement, complex system models of attitudes and polarization research. [ABSTRACT FROM AUTHOR]

Nanothermodynamics provides the theoretical foundation for understanding stable distributions of statistically independent subsystems inside larger systems. In this review, it is emphasized that extending ideas from nanothermodynamics to simplistic models improves agreement with the measured properties of many materials. Examples include non-classical critical scaling near ferromagnetic transitions, thermal and dynamic behavior near liquid–glass transitions, and the 1/f-like noise in metal films and qubits. A key feature in several models is to allow separate time steps for distinct conservation laws: one type of step conserves energy and the other conserves momentum (e.g., dipole alignment). This "orthogonal dynamics" explains how the relaxation of a single parameter can exhibit multiple responses such as primary, secondary, and microscopic peaks in the dielectric loss of supercooled liquids, and the crossover in thermal fluctuations from Johnson–Nyquist (white) noise at high frequencies to 1/f-like noise at low frequencies. Nanothermodynamics also provides new insight into three basic questions. First, it gives a novel solution to Gibbs' paradox for the entropy of the semi-classical ideal gas. Second, it yields the stable equilibrium of Ising's original model for finite-sized chains of interacting binary degrees of freedom ("spins"). Third, it confronts Loschmidt's paradox for the arrow of time, showing that an intrinsically irreversible step is required for maximum entropy and the second law of thermodynamics, not only in the thermodynamic limit but also in systems as small as N = 2 particles. [ABSTRACT FROM AUTHOR]

Quantum Reservoir Computing (QRC) offers potential advantages over classical reservoir computing, including inherent processing of quantum inputs and a vast Hilbert space for state exploration. Yet, the relation between the performance of reservoirs based on complex and many-body quantum systems and non-classical state features is not established. Through an extensive analysis of QRC based on a transverse-field Ising model we show how different quantum effects, such as quantum coherence and correlations, contribute to improving the performance in temporal tasks, as measured by the Information Processing Capacity. Additionally, we critically assess the impact of finite measurement resources and noise on the reservoir's dynamics in different regimes, quantifying the limited ability to exploit quantum effects for increasing damping and noise strengths. Our results reveal a monotonic relationship between reservoir performance and coherence, along with the importance of quantum effects in the ergodic regime. Quantum Reservoir Computing leverages the quantum properties of physical systems for solving temporal tasks. This study shows the importance of quantum effects, such as coherence and superposition, in the reservoir's performance for different dynamical regimes, while considering the impact of finite measurements and noisy environments. [ABSTRACT FROM AUTHOR]

Quantum algorithms are emerging tools in the design of functional materials due to their powerful solution space search capability. How to balance the high price of quantum computing resources and the growing computing needs has become an urgent problem to be solved. We propose a novel optimization strategy based on an active learning scheme that combines the Quantum-inspired Genetic Algorithm (QGA) with machine learning surrogate model regression. Using Random Forests as the surrogate model circumvents the time-consuming physical modeling or experiments, thereby improving the optimization efficiency. QGA, a genetic algorithm embedded with quantum mechanics, combines the advantages of quantum computing and genetic algorithms, enabling faster and more robust convergence to the optimum. Using the design of planar multilayer photonic structures for transparent radiative cooling as a testbed, we show superiority of our algorithm over the classical genetic algorithm (CGA). Additionally, we show the precision advantage of the Random Forest (RF) model as a flexible surrogate model, which relaxes the constraints on the type of surrogate model that can be used in other quantum computing optimization algorithms (e.g., quantum annealing needs Ising model as a surrogate). [ABSTRACT FROM AUTHOR]

We show that the quantum approximate optimization algorithm (QAOA) for higher-order, random coefficient, heavy-hex compatible spin glass Ising models has strong parameter concentration across problem sizes from 16 up to 127 qubits for p = 1 up to p = 5, which allows for computationally efficient parameter transfer of QAOA angles. Matrix product state (MPS) simulation is used to compute noise-free QAOA performance. Hardware-compatible short-depth QAOA circuits are executed on ensembles of 100 higher-order Ising models on noisy IBM quantum superconducting processors with 16, 27, and 127 qubits using QAOA angles learned from a single 16-qubit instance using the JuliQAOA tool. We show that the best quantum processors find lower energy solutions up to p = 2 or p = 3, and find mean energies that are about a factor of two off from the noise-free distribution. We show that p = 1 QAOA energy landscapes remain very similar as the problem size increases using NISQ hardware gridsearches with up to a 414 qubit processor. [ABSTRACT FROM AUTHOR]

Much is understood about 1-dimensional spin chains in terms of entanglement properties, physical phases, and integrability. However, the Lie algebraic properties of the Hamiltonians describing these systems remain largely unexplored. In this work, we provide a classification of all Lie algebras generated by the terms of 2-local spin chain Hamiltonians, or so-called dynamical Lie algebras, on 1-dimensional linear and circular lattice structures. We find 17 unique dynamical Lie algebras. Our classification includes some well-known models such as the transverse-field Ising model and the Heisenberg chain, and we also find more exotic classes of Hamiltonians that appear new. In addition to the closed and open spin chains, we consider systems with a fully connected topology, which may be relevant for quantum machine learning approaches. We discuss the practical implications of our work in the context of variational quantum computing, quantum control and the spin chain literature. [ABSTRACT FROM AUTHOR]

We present a collection of simulations of the Edwards–Anderson lattice spin glass at T = 0 to elucidate the nature of low-energy excitations over a range of dimensions that reach from physically realizable systems to the mean-field limit. Using heuristic methods, we sample the ground states of instances to determine their energies while eliciting excitations through manipulating boundary conditions. We exploit the universality of the phase diagram of bond-diluted lattices to make such a study in higher dimensions computationally feasible. As a result, we obtain a variety of accurate exponents for domain wall stiffness and finite-size corrections, which allow us to examine their dimensional behavior and their connection with predictions from mean-field theory. We also provide an experimentally testable prediction for the thermal-to-percolative crossover exponent in dilute lattice Ising spin glasses. [ABSTRACT FROM AUTHOR]

Quantum generative models have shown promise in fields such as quantum chemistry, materials science, and optimization. However, their practical utility is hindered by a significant challenge: the lack of interpretability. In this work, we introduce model inversion to enhance both the interpretability and controllability of quantum generative models. Model inversion allows for tracing generated quantum states back to their latent variables, revealing the relationship between input parameters and generated outputs. We apply this method to models generating ground states for Hamiltonians, such as the transverse-field Ising model (TFIM) and generalized cluster Hamiltonians, achieving interpretability control without retraining the model. Experimental results demonstrate that our approach can accurately guide the generated quantum states across different quantum phases. This framework bridges the gap between theoretical models and practical applications by providing transparency and fine-tuning capabilities, particularly in high-stakes environments like drug discovery and material design. [ABSTRACT FROM AUTHOR]

We study the zeros of the partition function in the complex temperature plane (Fisher zeros) and in the complex external field plane (Lee–Yang zeros) of a frustrated Ising model with competing nearest-neighbor ( J 1 > 0 ) and next-nearest-neighbor ( J 2 < 0 ) interactions on the honeycomb lattice. We consider the finite-size scaling (FSS) of the leading Fisher and Lee–Yang zeros as determined from a cumulant method and compare it to a traditional scaling analysis based on the logarithmic derivative of the magnetization ∂ ln 〈 | M | 〉 / ∂ β and the magnetic susceptibility χ. While for this model both FSS approaches are subject to strong corrections to scaling induced by the frustration, their behavior is rather different, in particular as the ratio R = J 2 / J 1 is varied. As a consequence, an analysis of the scaling of partition function zeros turns out to be a useful complement to a more traditional FSS analysis. For the cumulant method, we also study the convergence as a function of cumulant order, providing suggestions for practical implementations. The scaling of the zeros convincingly shows that the system remains in the Ising universality class for R as low as − 0.22 , where results from traditional FSS using the same simulation data are less conclusive. Hence, the approach provides a valuable additional tool for mapping out the phase diagram of models afflicted by strong corrections to scaling. [ABSTRACT FROM AUTHOR]

The full Heusler alloy Ga 2 MnCo, with its relatively low Curie temperature, is a promising candidate for magnetic refrigeration applications. Thus, a theoretical study using the mean-field theory based on the Bogoliubov inequality for the Gibbs free energy in the context of the Ising model is crucial for gaining a better understanding of the magnetic behavior of this material. We investigated the effects of magnetic anisotropy and exchange coupling on the ground-state phase diagrams, identifying the most stable configurations. Additionally, we obtained the magnetic properties at finite temperature and showed that only second-order phase transitions occur for any values of the theoretical Hamiltonian parameters. The model describes rich phase transitions, including first- and second-order phase transitions, as well as a critical end-point. The critical behavior of the system arises from the competition between exchange interaction and magnetic anisotropy. [ABSTRACT FROM AUTHOR]

We study a mean-field spin model with three- and two-body interactions. The equilibrium measure for large volumes is shown to have three pure states, the phases of the model. They include the two with opposite magnetization and an unpolarized one with zero magnetization, merging at the critical point. We prove that the central limit theorem holds for a suitably rescaled magnetization, while its violation with the typical quartic behavior appears at the critical point. [ABSTRACT FROM AUTHOR]

We introduce and analyze a natural class of nonlinear dynamics for spin systems such as the Ising model. This class of dynamics is based on the framework of mass action kinetics, which models the evolution of systems of entities under pairwise interactions, and captures a number of important nonlinear models from various fields, including chemical reaction networks, Boltzmann's model of an ideal gas, recombination in population genetics and genetic algorithms. In the context of spin systems, it is a natural generalization of linear dynamics based on Markov chains, such as Glauber dynamics and block dynamics, which are by now well understood. However, the inherent nonlinearity makes the dynamics much harder to analyze, and rigorous quantitative results so far are limited to processes which converge to essentially trivial stationary distributions that are product measures. In this paper we provide the first quantitative convergence analysis for natural nonlinear dynamics in a combinatorial setting where the stationary distribution contains non-trivial correlations, namely spin systems at high temperatures. We prove that nonlinear versions of both the Glauber dynamics and the block dynamics converge to the Gibbs distribution of the Ising model (with given external fields) in times O (n log n) and O (log n) respectively, where n is the size of the underlying graph (number of spins). Given the lack of general analytical methods for such nonlinear systems, our analysis is unconventional, and combines tools such as information percolation (due in the linear setting to Lubetzky and Sly), a novel coupling of the Ising model with Erdős-Rényi random graphs, and non-traditional branching processes augmented by a "fragmentation" process. Our results extend immediately to any spin system with a finite number of spins and bounded interactions. [ABSTRACT FROM AUTHOR]

Quantum architecture search (QAS) has attracted increasing attention owing to its remarkable ability to automate the design of quantum circuits for variational quantum algorithms (VQAs). However, evaluating the performance of numerous quantum circuits is essential to provide feedback for the search strategy, which inevitably renders QAS computationally expensive. Performance predictors have emerged as highly efficient evaluation methods to mitigate this challenge. However, the performance predictor faces a critical challenge in reducing the required number of circuit‐performance pairs for training. This study encodes circuit architecture by representing a quantum circuit as a relational graph that emphasizes message exchange. Subsequently, valuable information about circuit architecture is extracted through three types of graph measures, including distance‐based, degree‐based, and cluster‐based measures. The graph measures define a smooth space related to circuit performance, facilitating the training of the performance predictor. The effectiveness of the proposed method is assessed across three tasks within variational quantum eigensolvers (VQE): identifying the ground states of the Transverse Field Ising Model (TFIM), the Heisenberg model, and the BeH2$\text{BeH}_2$ molecule. The simulation results demonstrate notable enhancements in predictive accuracy achieved by our method, coupled with a substantial reduction in the required number of training samples for the predictor. [ABSTRACT FROM AUTHOR]

We first present a formalism that incorporates the input-output formalism and the linear response theory to employ cavity-magnon-polariton coupling as a spectroscopic tool for investigating strongly hybridized electro-nuclear spin excitations. A microscopic relation between the generalized susceptibility and the scattering parameter | S 11 | in strongly hybridized cavity-magnon-polariton systems has been derived without resorting to semi-classical approximations. The formalism is then applied to both analyze and simulate a specific systems comprising a model quantum Ising magnet ( LiHoF 4 ) and a high-finesse 3D re-entrant cavity resonator. Quantitative information on the electro-nuclear spin states in LiHoF 4 is extracted, and the experimental observations across a broad parameter range were numerically reproduced, including an external magnetic field traversing a quantum critical point. The method potentially opens a new avenue not only for further studies on the quantum phase transition in LiHoF 4 but also for a wide range of complex magnetic systems. [ABSTRACT FROM AUTHOR]

Recent advances in the study of cobaltites have unveiled their potential as a promising platform for realizing Kitaev physics in honeycomb systems and the Ising model in weakly coupled chain materials. In this manuscript, we explore the magnetic properties of pyroxene SrCoGe2O6 using a combination of neutron scattering, ab initio methods, and linear spin-wave theory. Through careful examination of inelastic neutron scattering powder spectra, we propose a modified Kitaev model to accurately describe the twisted chains of edge-sharing octahedra surrounding Co2+ ions. The extended Kitaev–Heisenberg model, including a significant anisotropic bonddependent exchange term with K /|J| = 0.96, is identified as the key descriptor of the magnetic interactions in SrCoGe2O6. Furthermore, our heat capacity measurements reveal an effect of an external magnetic field (approximately 13 T) which shifts the system from a fragile antiferromagnetic ordering with TN = 9 K to a field-induced state. We argue that pyroxenes, particularly those modified by substituting Ge with Si and its less extended p orbitals, emerge as a platform for the Kitaev model. This opens up possibilities for advancing our understanding of Kitaev physics. [ABSTRACT FROM AUTHOR]

We first present a formalism that incorporates the input-output formalism and the linear response theory to employ cavity-magnon-polariton coupling as a spectroscopic tool for investigating strongly hybridized electro-nuclear spin excitations. A microscopic relation between the generalized susceptibility and the scattering parameter | S 11 | in strongly hybridized cavity-magnon-polariton systems has been derived without resorting to semi-classical approximations. The formalism is then applied to both analyze and simulate a specific systems comprising a model quantum Ising magnet ( LiHoF 4 ) and a high-finesse 3D re-entrant cavity resonator. Quantitative information on the electro-nuclear spin states in LiHoF 4 is extracted, and the experimental observations across a broad parameter range were numerically reproduced, including an external magnetic field traversing a quantum critical point. The method potentially opens a new avenue not only for further studies on the quantum phase transition in LiHoF 4 but also for a wide range of complex magnetic systems. [ABSTRACT FROM AUTHOR]

This study introduces the long‐range Ising model from statistical mechanics to the performance‐based earthquake engineering (PBEE) framework for regional seismic damage analysis. The application of the PBEE framework at a regional scale involves estimating the damage states (DSs$DS\mathrm{s}$) of numerous structures, typically performed using fragility function‐based stochastic simulations. However, these simulations often assume conditional independence or employ simplistic dependency models among the DSs$DS\mathrm{s}$ of structures, leading to significant misrepresentation of regional risk. The Ising model addresses this issue by converting the available information on binary DSs$DS\mathrm{s}$ (safe or failure) into a joint probability mass function, leveraging the principle of maximum entropy. The Ising model offers two main benefits: (1) it requires only the first‐ and second‐order cross‐moments, enabling seamless integration with the existing PBEE framework, and (2) it provides meaningful physical interpretations of the model parameters, facilitating the uncovering of insights not apparent from data. To demonstrate the proposed method, we applied the Ising model to 156 buildings in Antakya, Turkey, using post‐hazard damage evaluation data, and to 182 buildings in Pacific Heights, San Francisco, using simulated data from the Regional Resilience Determination tool. In both instances, the Ising model accurately reproduces the provided information and generates meaningful insights into regional damage. The study also investigates the change in Ising model parameters under varying earthquake magnitudes, along with the mean‐field approximation, further facilitating the applicability of the proposed approach. [ABSTRACT FROM AUTHOR]

Genetically diverse populations can increase plant resistance to natural enemies. Yet, beneficial genotype pairs remain elusive due to the occurrence of positive or negative effects of mixed planting on plant resistance, respectively called associational resistance or susceptibility. Here, we identify key genotype pairs responsible for associational resistance to herbivory using the genome-wide polymorphism data of the plant species Arabidopsis thaliana. To quantify neighbor interactions among 199 genotypes grown in a randomized block design, we employ a genome-wide association method named "Neighbor GWAS" and genomic prediction inspired by the Ising model of magnetics. These analyses predict that 823 of the 19,701 candidate pairs can reduce herbivory in mixed planting. We planted three pairs with the predicted effects in mixtures and monocultures, and detected 18–30% reductions in herbivore damage in the mixed planting treatment. Our study shows the power of genomic prediction to assemble genotype mixtures with positive biodiversity effects. Identifying pairs of genotypes that perform better in mixture than monoculture is important for increasing crop yields. Using the model species Arabidopsis thaliana, this study provides a proof of principle of how such beneficial genotype pairs could be found using genome-wide association studies. [ABSTRACT FROM AUTHOR]

We present a collection of simulations of the Edwards-Anderson lattice spin glass at T = 0 to elucidate the nature of low-energy excitations over a range of dimensions that reach from physically realizable systems to the mean-field limit. Using heuristic methods, we sample the ground states of instances to determine their energies while eliciting excitations through manipulating boundary conditions. We exploit the universality of the phase diagram of bond-diluted lattices to make such a study in higher dimensions computationally feasible. As a result, we obtain a variety of accurate exponents for domain wall stiffness and finite-size corrections, which allow us to examine their dimensional behavior and their connection with predictions from mean-field theory. We also provide an experimentally testable prediction for the thermal-to-percolative crossover exponent in dilute lattice Ising spin glasses. [ABSTRACT FROM AUTHOR]

Global quantum discord (GQD) refers to the number of quantum correlations present in the entire quantum many-body system, rather than just between two subsystems. Here, we utilize GQD to characterize quantum phase transitions in an Ising chain subjected to both transverse and longitudinal magnetic fields. We investigate the effects of the transverse magnetic field h x , longitudinal magnetic field h z , and temperature T on the properties of GQD while keeping the coupling strength J between spins constant. We show that we can perfectly illustrate the critical points of the model by analyzing the singularity of GQD. We find that the GQD exhibits an increase as the system size N increases, regardless of whether the temperature is zero or finite. We present the phase diagram of a mixed Ising model under the combined influence of h x and h z . Moreover, we show that we can use the features of GQD at lower temperatures to identify QPTs in quantum many-body systems and determine their critical points, as achieving absolute zero temperatures is practically impossible. Additionally, we show that GQD both at zero and finite temperatures show a linear behavior of the system size N, i.e., G = k N + b , in which k and b are the fitting parameters. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the phenomena of order-disorder phase transition and the universality of the majority-rule model defined on three complex networks, namely the Barabási–Albert, Watts–Strogatz and Erdős–Rényi networks. Assume each agent holds two possible opinions randomly distributed across the networks' nodes. Agents adopt anticonformity and independence behaviors, represented by the probability p, where with a probability p, agents adopt anticonformity or independence behavior. Based on our numerical simulation results and finite-size scaling analysis, it is found that the model undergoes a continuous phase transition for all networks, with critical points for the independence model greater than those for the anticonformity model in all three networks. We obtain critical exponents identical to the opinion dynamics model defined on a complete graph, indicating that the model exhibits the same universality class as the mean-field Ising model. [ABSTRACT FROM AUTHOR]

The motivation for this paper is the analysis of the fixed-density Ising lattice gas in the presence of a gravitational field. This is seen as a particular instance of an Ising model with a slowly varying magnetic field in the fixed magnetization ensemble. We first characterize the typical magnetization profiles in the regime in which the contribution of the magnetic field competes with the bulk energy term. We then discuss in more detail the particular case of a gravitational field and the arising interfacial phenomena. In particular, we identify the macroscopic profile and propose several conjectures concerning the interface appearing in the phase coexistence regime. The latter are supported by explicit computations in an effective model. Finally, we state some conjectures concerning equilibrium crystal shapes in the presence of a gravitational field, when the latter contributes to the energy only to surface order. [ABSTRACT FROM AUTHOR]

Many-body quantum dynamics defined on a spatial lattice and in discrete time—either as stroboscopic Floquet systems or quantum circuits—has been an active area of research for several years. Being discrete in space and time, a natural question arises: when can such a model be viewed as evolving unitarily in space as well as in time? Models with this property, which sometimes goes by the name space-time duality, have been shown to have a number of interesting features related to entanglement growth and correlations. One natural way in which the property arises in the context of (brickwork) quantum circuits is by choosing dual unitary gates: two site operators that are unitary in both the space and time directions. We introduce a class of models with q states per site, defined on the square lattice by a complex partition function and paremeterized in terms of q × q Hadamard matrices, that have the property of space-time duality. These may interpreted as particular dual unitary circuits or stroboscopically evolving systems, and generalize the well studied self-dual kicked Ising model. We explore the operator dynamics in the case of Clifford circuits, making connections to Clifford cellular automata (Schlingemann et al 2008 J. Math. Phys. 49 112104) and in the q → ∞ limit to the classical spatiotemporal cat model of many body chaos (Gutkin et al 2021 Nonlinearity 34 2800). We establish integrability and the corresponding conserved charges for a large subfamily and show how the long-range entanglement protocol discussed in the recent paper (Lotkov et al 2022 Phys. Rev. B 105 144306) can be reinterpreted in purely graphical terms and directly applied here. [ABSTRACT FROM AUTHOR]

Thermodynamic extrinsic curvature is a new mathematical tool in thermodynamic geometry. By using the thermodynamic extrinsic curvature, one may obtain a more complete geometric representation of the critical phenomena and thermodynamics. We introduce nonperturbative thermodynamic extrinsic curvature of an ideal two-dimensional gas of anyons. Using extrinsic curvature, we find new fixed points in nonperturbative thermodynamics of the anyon gas that particles behave as semions. Here, we investigate the critical behavior of thermodynamic extrinsic curvature of two-dimensional Kagome Ising model near the critical point β c = (k B T c) − 1 in a constant magnetic field and show that it behaves as | β − β c | α with α = 0 , where α denotes the critical exponent of the specific heat. Then, we consider the three-dimensional spherical model and show that the scaling behavior is | β − β c | α , where α = − 1. Finally, using a general argument, we show that extrinsic curvature K has two different scaling behaviors for positive and negative α. For α > 0 , our results indicate that K ∼ | β − β c | 1 2 (α − 2) . However, for α < 0 , we found a different scaling behavior, where K ∼ | β − β c | α . [ABSTRACT FROM AUTHOR]

For d ≥ 3 , we study the Ising model on Z d with random field given by { ϵ h v : v ∈ Z d } where h v 's are independent normal variables with mean 0 and variance 1. We show that for any T < T c (here T c is the critical temperature without disorder), long range order exists as long as ϵ is sufficiently small depending on T . Our work extends previous results of Imbrie (1985) and Bricmont–Kupiainen (1988) from the very low temperature regime to the entire low temperature regime. [ABSTRACT FROM AUTHOR]

Cardiac muscle contraction is initiated by an elementary Ca signal (called Ca spark) which is achieved by collective action of Ca release channels in a cluster. The mechanism of this synchronization remains uncertain. We approached Ca spark activation as an emergent phenomenon of an interactive system of release channels. We constructed a weakly lumped Markov chain that applies an Ising model formalism to such release channel clusters and probable open channel configurations and demonstrated that spark activation is described as a system transition from a metastable to an absorbing state, analogous to the pressure required to overcome surface tension in bubble formation. This yielded quantitative estimates of the spark generation probability as a function of various system parameters. We performed numerical simulations to find spark probabilities as a function of sarcoplasmic reticulum Ca concentration, obtaining similar values for spark activation threshold as our analytic model, as well as those reported in experimental studies. Our parametric sensitivity analyses also showed that the spark activation threshold decreased as Ca sensitivity of RyR activation and RyR cluster size increased. [ABSTRACT FROM AUTHOR]

Sparse connectivity of a superconducting quantum computer results in large experimental overheads of SWAP gates. In this study, we consider employing a virtual two-qubit gate (VTQG) as an error suppression technique. The VTQG enables a non-local operation between a pair of distant qubits using only single qubit gates and projective measurements. Here, we apply the VTQG to the digital quantum simulation of the transverse-field Ising model on an IBM quantum computer to suppress the errors due to the noisy two-qubit operations. We present an effective use of VTQG, where the reduction in multiple SWAP gates results in increasing the fidelity of output states. The obtained results indicate that the VTQG can be useful for suppressing the errors due to additional SWAP gates. In our experiments, we have observed one order of magnitude improvement in accuracy for the quantum simulation of the transverse-field Ising model with 8 qubits. Finally, we have demonstrated an efficient implementation of the VTQG by utilizing dynamic circuits. This scheme reduces experimental overheads for implementing m VTQGs from O (10 m) to O (6 m). [ABSTRACT FROM AUTHOR]

Yiwang Zhou,1 Madeline R Horan,2 Samira Deshpande,1 Kirsten K Ness,2 Melissa M Hudson,3 I-Chan Huang,2,&ast; Deokumar Srivastava1,&ast; 1Department of Biostatistics, St. Jude Children’s Research Hospital, Memphis, TN, USA; 2Department of Epidemiology and Cancer Control, St. Jude Children’s Research Hospital, Memphis, TN, USA; 3Department of Oncology, St. Jude Children’s Research Hospital, Memphis, TN, USA&ast;These authors contributed equally to this workCorrespondence: Yiwang Zhou, Department of Biostatistics, St. Jude Children’s Research Hospital, 262 Danny Thomas Place, Mail Stop 768, Memphis, Tennessee, TN 38105, USA, Tel +1 901-595-6736, Email yiwang.zhou@stjude.orgPurpose: Childhood cancer survivors experience interconnected symptoms, patterns of which can be elucidated by network analysis. However, current symptom networks are constructed based on the average survivors without considering individual heterogeneities. We propose to evaluate personal symptom network estimation using the Ising model with covariates through simulations and estimate personal symptom network for adult childhood cancer survivors.Patients and Methods: We adopted the Ising model with covariates to construct networks by employing logistic regressions for estimating associations between binary symptoms. Simulation experiments assessed the robustness of this method in constructing personal symptom network. Real-world data illustration included 1708 adult childhood cancer survivors from the St. Jude Lifetime Cohort Study (SJLIFE), a retrospective cohort study with prospective follow-up to characterize the etiology and late effects for childhood cancer survivors. Patients’ baseline symptoms in 10 domains (cardiac, pulmonary, sensation, nausea, movement, pain, memory, fatigue, anxiety, depression) and individual characteristics (age, sex, race/ethnicity, attained education, personal income, and marital status) were self-reported using survey. Treatment variables (any chemo or radiation therapy) were obtained from medical records. Personal symptom network of 10 domains was estimated using the Ising model, incorporating individual characteristics and treatment data.Results: Simulations confirmed the robustness of the Ising model with covariates in constructing personal symptom networks. Real-world data analysis identified age, sex, race/ethnicity, education, marital status, and treatment (any chemo and radiation therapy) as major factors influencing symptom co-occurrence. Older childhood cancer survivors showed stronger cardiac-fatigue associations. Survivors of racial/ethnic minorities had stronger pain-fatigue associations. Female survivors with above-college education demonstrated stronger pain-anxiety associations. Unmarried survivors who received radiation had stronger association between movement and memory problems.Conclusion: The Ising model with covariates accurately estimates personal symptom networks. Individual heterogeneities exist in symptom co-occurrence patterns for childhood cancer survivors. The estimated personal symptom network offers insights into interconnected symptom experiences.Keywords: bootstrap testing, individual heterogeneity, Ising model, network analysis, sociodemographic

In this review, we discuss currents in celestial CFT and the consistency of their naïve symmetry algebras. In particular, we study in detail the Jacobi identity and the double residue condition for soft insertions, hard momentum space insertions, and hard celestial insertions. In the latter case, we introduce the notion of a "hard current" in CFT and work through examples in the 2D critical Ising model. The current algebra of hard insertions in pure Einstein gravity is a slight conceptual generalization of the familiar w 1 + ∞ -wedge current algebra. We also review branch cut terms in the celestial OPE, which indicate new primary content and were previously missed until recently. We work through an explicit toy example illustrating the mechanism by which such branch cut terms can arise. These branch cut terms prevent a symmetry interpretation but are fully compatible with a consistent OPE. [ABSTRACT FROM AUTHOR]

In mathematical statistical mechanics, Gibbs measures have been designed to represent equilibrium states and to model phase transition. In the literature, Gibbs measures associated with the Ising model on Cayley trees have been extensively studied. However, the Ising model has not been studied on (i,k)-ary trees before. In this paper, the phase transition problem is investigated for the Ising model on (i,k)-ary trees. Specifically, the model on Γ(1,k) and Γ(2,3), respectively, displays three distinct translation-invariant Gibbs measures in both the ferromagnetic and anti-ferromagnetic states, whereas the traditional Ising model lacks translation-invariant Gibbs measures in the anti-ferromagnetic state. Moreover, non-translation invariant Gibbs measures are constructed as well. Furthermore, for the considered model, the standard free energy does not exist, in contrast to its existence over regular trees. [ABSTRACT FROM AUTHOR]

Cornerstones of the Cellular Automaton Interpretation of Quantum Mechanics are its ontological states that evolve by permutations, in this way never creating would-be quantum mechanical superposition states. We review and illustrate this with a classical Ising spin chain. It is shown that it can be related to the Weyl equation in the continuum limit. Yet, the model of discrete spins or bits unavoidably becomes a model of qubits by generating superpositions, if only slightly deformed. We study modifications of its signal velocity which, however, do not relate to mass terms. To incorporate the latter, we consider the Dirac equation in 1+1 dimensions and sketch an underlying discrete deterministic "necklace of necklaces" automaton that qualifies as ontological. [ABSTRACT FROM AUTHOR]

In this paper, we studied the spin-3/2 Ising model of diluted graphene-like monolayer under a non-equilibrium state by using Monte Carlo (MC) simulation. We conducted a comprehensive analysis of the temperature-dependent magnetization curves, susceptibility, critical temperature, and hysteresis loops taking into account various factors such as the anisotropy, exchange coupling, external magnetic field, and shell atom concentration. We also compared our findings to various existing theoretical works and obtained a strong quantitative alignment with certain theoretical predictions and experimental outcomes. [ABSTRACT FROM AUTHOR]