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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]

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]

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]

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]

Inspired by the 1995 paper of Baake–Grimm–Pisani, we aim to explain the empirical observation that the distribution of Lee–Yang zeros corresponding to a one-dimensional Ising model appears to follow the gap labelling theorem. This follows by combining two main ingredients: first, the relation between the transfer matrix formalism for the 1D Ising model and an ostensibly unrelated matrix formalism generating the Szegő recursion for orthogonal polynomials on the unit circle, and second, the gap labelling theorem for CMV matrices. [ABSTRACT FROM AUTHOR]

Obtaining all perfect matchings of a graph is a tough problem in graph theory, and its complexity belongs to the #P-Complete class. The problem is closely related to combinatorics, marriage matching problems, dense subgraphs, the Gaussian boson sampling, chemical molecular structures, and dimer physics. In this paper, we propose a quadratic unconstrained binary optimization formula of the perfect matching problem and translate it into the quantum Ising model. We can obtain all perfect matchings by mapping them to the ground state of the quantum Ising Hamiltonian and solving it with the variational quantum eigensolver. Adjusting the model’s parameters can also achieve the maximum or minimum weighted perfect matching. The experimental results on a superconducting quantum computer of the Origin Quantum Computing Technology Company show that our model can encode 2n dimensional optimization space with only O(n) qubits consumption and achieve a high success probability of the ground state corresponding to all perfect matchings. In addition, the further simulation results show that the model can support a scale of more than 14 qubits, effectively resist the adverse effects of noise, and obtain a high success probability at a shallow variational depth. This method can be extended to other combinatorial optimization problems. [ABSTRACT FROM AUTHOR]

Summary Oscillator‐based Ising machines (OIMs) particularly those realized in complementary metal oxide semiconductor (CMOS) have gained popularity for solving combinatorial optimization problems (COPs) in recent years due to its scalability, low‐power consumption, and room temperature operation. The implemented OIMs have thus far focused on solving optimization problems with a single global minima. However, real‐life optimization problems often have multiple solutions. In this paper, we propose a generalized approach to solve COPs with single (without contention), as well as multiple (with contention) solutions using frequency tunable CMOS ring oscillator (ROSC)‐based Ising machine. A capacitive frequency tunable CMOS ring‐oscillator coupled with an internal subharmonic injection locking (SHIL) generator realized using 14‐nm FinFET models works as Ising spin in the proposed approach. We demonstrate how frequency tuning can help in attaining good quality results and also determine all possible solutions of COP with contention. We also propose a generalized algorithm for monitoring the states of the oscillator network to indicate tuning necessity and extract solutions from the oscillator's output irrespective of the type of COP. [ABSTRACT FROM AUTHOR]

We develop a theory of the critical point of the ferromagnetic Ising model, whose basic objects are the ergodic (pure) states of the infinite system. It proves the existence of anomalous critical fluctuations, for dimension ν = 2 and, under a standard assumption, for ν = 3 , for the model with nearest-neighbor interaction, in a way which is consistent with the probabilistic approach of Cassandro, Jona-Lasinio, and several others, reviewed in Jona-Lasinio's article in Phys. Rep. 352,439 (2001). We propose to single out the state at the critical temperature T c , among the ergodic thermal states associated to temperatures 0 ≤ T ≤ T c , by a condition of non-summable clustering of the connected two-point function. The analogous condition on the connected (2r)- point functions, for r ≥ 2 , together with a scaling hypothesis, natural within our framework, proves that the (macroscopic) fluctuation state is quasi-free, after a proper rescaling, also at the critical temperature, in agreement with a theorem by Cassandro and Jona-Lasinio, whose proof is, however, shown to be incomplete. Other subjects treated include topics relating to universality, including spontaneous breaking of continuous symmetries and violations of universality in problems of energetic and dynamic stability. [ABSTRACT FROM AUTHOR]

Jamming is an athermal transition between flowing and rigid states in amorphous systems such as granular matter, colloidal suspensions, complex fluids and cells. The jamming transition seems to display mixed aspects of a first-order transition, evidenced by a discontinuity in the coordination number, and a second-order transition, indicated by power-law scalings and diverging lengths. Here we demonstrate that jamming is a first-order transition with quenched disorder in cyclically sheared systems with quasistatic deformations, in two and three dimensions. Based on scaling analyses, we show that fluctuations of the jamming density in finite-sized systems have important consequences on the finite-size effects of various quantities, resulting in a square relationship between disconnected and connected susceptibilities, a key signature of the first-order transition with quenched disorder. This study puts the jamming transition into the category of a broad class of transitions in disordered systems where sample-to-sample fluctuations dominate over thermal fluctuations, suggesting that the nature and behavior of the jamming transition might be better understood within the developed theoretical framework of the athermally driven random-field Ising model. Jamming in amorphous systems is an athermal transition characterized by mixed first-order and second-order aspects. Authors demonstrate that jamming is a first-order transition with quenched disorder, revealing significant finite-size effects and a square relationship between disconnected and connected susceptibilities in cyclically sheared systems. [ABSTRACT FROM AUTHOR]

Energy landscape analysis is a data‐driven method to analyse multidimensional time series, including functional magnetic resonance imaging (fMRI) data. It has been shown to be a useful characterization of fMRI data in health and disease. It fits an Ising model to the data and captures the dynamics of the data as movement of a noisy ball constrained on the energy landscape derived from the estimated Ising model. In the present study, we examine test–retest reliability of the energy landscape analysis. To this end, we construct a permutation test that assesses whether or not indices characterizing the energy landscape are more consistent across different sets of scanning sessions from the same participant (i.e. within‐participant reliability) than across different sets of sessions from different participants (i.e. between‐participant reliability). We show that the energy landscape analysis has significantly higher within‐participant than between‐participant test–retest reliability with respect to four commonly used indices. We also show that a variational Bayesian method, which enables us to estimate energy landscapes tailored to each participant, displays comparable test–retest reliability to that using the conventional likelihood maximization method. The proposed methodology paves the way to perform individual‐level energy landscape analysis for given data sets with a statistically controlled reliability. [ABSTRACT FROM AUTHOR]

In this paper, we study Feynman checkers, one of the most elementary models of electron motion. It is also known as a one-dimensional quantum walk or an Ising model at an imaginary temperature. We add the simplest non-trivial electromagnetic field and find the limits of the resulting model for small lattice step and large time, analogous to the results by Narlikar from 1972 and Grimmet–Jason–Scudo from the 2000s. It turns out that the limits in the model with the added field are obtained from the ones without field by mass renormalization. Also, we find an exact solution of the resulting model. [ABSTRACT FROM AUTHOR]

Lattice models exhibit significant potential in investigating phase transitions, yet they encounter numerous computational challenges. To address these issues, this study introduces a Monte Carlo-based approach that transforms lattice models into a network model with intricate inter-node correlations. This framework enables a profound analysis of Ising, JQ, and XY models. By decomposing the network into a maximum entropy component and a conservative component, under the constraint of detailed balance, this work derives an estimation formula for the temperature-dependent magnetic induction in Ising models. Notably, the critical exponent β in the Ising model aligns well with the established results, and the predicted phase transition point in the three-dimensional Ising model exhibits a mere 0.7% deviation from numerical simulations. [ABSTRACT FROM AUTHOR]

The growing role of artificial intelligence (AI) in our society presents both benefits and challenges. To delve deeper into this, we suggest a simulation model that mimics a human–AI ecosystem. This model considers various factors, such as biased actions and multiple-agent interactions ranging from two to five agents. For instance, it includes situations where four humans engage with AI or where four AI systems interact with a human. Our main goal is to investigate how the number of AI systems in the ecosystem influences its dynamics. Our findings revealed that even slight variations in the presence of AI can cause significant changes in the system's behavior. These shifts can push the system to distinct opposing outcomes or leave it in a state of uncertainty. [ABSTRACT FROM AUTHOR]

Fractals are ubiquitous in the natural world, and their connection with phase transitions has been widely observed. This study investigates mechanisms of fractal formation from the perspective of phase transitions. A novel set of probability calculation methods is introduced to establish a direct link between fractals and phase transitions. Notably, in the Ising model, a specific category of boundary lattice points undergoes a phase transition when the associated weight reaches ∼0.4. The identified correlation between phase transitions and fractals suggests the emergence of fractal structures at this critical weight. This paper offers supporting evidence for this conclusion through the deliberate manipulation of the proposed probability-based method. This research contributes to a deeper understanding of the interplay between fractals and phase transitions, providing valuable insights for further exploration in diverse scientific domains. [ABSTRACT FROM AUTHOR]

We study applications of the connection between the partition functions of the Potts models and Tutte polynomials: it is demonstrated how the Kramers–Wannier duality can be derived from the Tutte duality. Using the "contraction–elimination" relation and the Biggs formalism, we derive the high-temperature expansion and discuss possible methods for generalizing the Kramers–Wannier duality to models on nonplanar graphs. [ABSTRACT FROM AUTHOR]

We apply a real-space block renormalization group approach to study the critical properties of the random transverse-field Ising spin chain with multispin interactions. First, we recover the known properties of the traditional model with two-spin interactions by applying the renormalization approach for the arbitrary size of the block. For the model with three-spin couplings, we calculate the critical point and demonstrate that the phase transition is controlled by an infinite disorder fixed point. We have determined the typical correlation-length critical exponent, which seems to be different from that of the random transverse Ising chain with nearest-neighbor couplings. Thus, this model represents a new infinite disorder universality class. [ABSTRACT FROM AUTHOR]

We present a new combinatorial approach to the Ising model incorporating arbitrary bond weights on planar graphs. In contrast to existing methodologies, the exact free energy is expressed as the determinant of a set of ordered and disordered operators defined on a planar graph and the corresponding dual graph, respectively, thereby explicitly demonstrating the Kramers–Wannier duality. The implications of our derived formula for the Random-Bond Ising Model are further elucidated. [ABSTRACT FROM AUTHOR]

In recent duration, exponential internet growth usage has necessitated robust methods for securing data during transmission. Image encryption has emerged as a crucial technique to prevent unauthorized access and manipulation of digital content. This study introduces a novel encryption method that enhances image security through a two-stage process. The first stage involves substituting and shuffling plain image pixels using a set of random numbers generated by the ISING model, where these numbers are described as a sequence of movements. In the second stage, pixel values are permuted using the Gyrator transformation, resulting in a ciphered image. Extensive numerical simulations have been conducted to calculate the effectiveness of the suggested method. The results confirm the method's efficacy, demonstrating significant improvements in security and robustness compared to existing encryption techniques. Statistical analyses further prove the advantages of using the confusion and diffusion properties for improving the proposed method. The proposed method represents a substantial improvement in the field of image encryption, presenting a secure and reliable solution for protecting digital images. [ABSTRACT FROM AUTHOR]

Deep neural networks have been used to solve Ising models, including autoregressive neural networks, convolutional neural networks, recurrent neural networks, and graph neural networks. Learning probability distributions of energy configuration or finding ground states of disordered, fully connected Ising models is essential for statistical mechanics and NP-hard problems. Despite tremendous efforts, neural network architectures with abilities to high-accurately solve these intractable problems on larger systems remain a challenge. Here we propose a variational autoregressive architecture with a message passing mechanism, which effectively utilizes the interactions between spin variables. The architecture trained under an annealing framework outperforms existing neural network-based methods in solving several prototypical Ising spin Hamiltonians, especially for larger systems at low temperatures. The advantages also come from the great mitigation of mode collapse during training process. Considering these difficult problems to be solved, our method extends computational limits of unsupervised neural networks to solve combinatorial optimization problems. Ising problems are ubiquitous in physics, hence the exploration of new methods to tackle Ising problems with large scale and dense connectivity is of great interest. The authors propose a variational autoregressive architecture with a message passing mechanism that uses the interactions between spin variables, while previous methods build on the correlations only. [ABSTRACT FROM AUTHOR]

Porphyrin‐based metal‐organic frameworks (MOFs) have received great attention for solar photochemistry applications. Manipulating the direction of energy (exciton) migration plays an essential role in boosting the light‐harvesting efficiency of porphyrin‐based MOFs. Here, based on the time‐dependent exciton‐exciton annihilation rate, an optical control of directional exciton migration is demonstrated in cobalt‐porphyrin surface‐supported MOF nanofilms (Co‐TCPP SURMOFs). Utilizing photocarrier densities or lattice temperature as the control knob, the dynamic form of exciton migration in Co‐TCPP SURMOFs can be switched between the nearest‐neighbor 1D interaction and the quasi‐isotropic 2D interaction, which is well explained using a diffusion model of exciton‐exciton scattering. This results provide an optical approach to regulating exciton migration in MOFs, which enhances understanding of the excitonic behavior in artificial light harvesters. [ABSTRACT FROM AUTHOR]

While Ising criticality in classical liquids has been firmly established both theoretically and experimentally, much less is known about criticality in liquids in which the growth of the correlation length is frustrated by finite-size effects. A theoretical approach for dealing with this issue is the random-field Ising model (RFIM). While experimental critical-exponent values have been reported for magnetic samples (here, we consider γ , ν and η), little experimental information is available for critical fluctuations in corresponding liquid systems. In this paper, we present a study on a binary liquid consisting of 3-methyl pyridine and heavy water in a very light-weight porous gel. We find that the experimental results are in agreement with the theoretical predictions from the RFIM. [ABSTRACT FROM AUTHOR]

The Biswas–Chatterjee–Sen (BChS) model of opinion dynamics has been studied on three-dimensional Solomon networks by means of extensive Monte Carlo simulations. Finite-size scaling relations for different lattice sizes have been used in order to obtain the relevant quantities of the system in the thermodynamic limit. From the simulation data it is clear that the BChS model undergoes a second-order phase transition. At the transition point, the critical exponents describing the behavior of the order parameter, the corresponding order parameter susceptibility, and the correlation length, have been evaluated. From the values obtained for these critical exponents one can confidently conclude that the BChS model in three dimensions is in a different universality class to the respective model defined on one- and two-dimensional Solomon networks, as well as in a different universality class as the usual Ising model on the same networks. [ABSTRACT FROM AUTHOR]

We prove, under an assumption on the critical points of a real‐valued function, that the symmetric Ising perceptron exhibits the 'frozen 1‐RSB' structure conjectured by Krauth and Mézard in the physics literature; that is, typical solutions of the model lie in clusters of vanishing entropy density. Moreover, we prove this in a very strong form conjectured by Huang, Wong, and Kabashima: a typical solution of the model is isolated with high probability and the Hamming distance to all other solutions is linear in the dimension. The frozen 1‐RSB scenario is part of a recent and intriguing explanation of the performance of learning algorithms by Baldassi, Ingrosso, Lucibello, Saglietti, and Zecchina. We prove this structural result by comparing the symmetric Ising perceptron model to a planted model and proving a comparison result between the two models. Our main technical tool towards this comparison is an inductive argument for the concentration of the logarithm of number of solutions in the model. [ABSTRACT FROM AUTHOR]

We study the dimer and Ising models on a finite planar weighted graph with periodic-antiperiodic boundary conditions, i.e. a graph Γ in the Klein bottle K. Let Γmn denote the graph obtained by pasting m rows and n columns of copies of Γ, which embeds in K for n odd and in the torus T2 for n even. We compute the dimer partition function Zmn of Γmn for n odd, in terms of the well-known characteristic polynomial P of Γ12⊂T² together with a new characteristic polynomial R of Γ⊂K. Using this result together with work of Kenyon, Sun and Wilson [arXiv:1310.2603], we show that in the bipartite case, this partition function has the asymptotic expansion logZmn=mnf0/2+fsc+o(1), for m,n tending to infinity and m/n bounded below and above, where f0 is the bulk free energy for Γ12⊂T² and fsc an explicit finite-size correction term. The remarkable feature of this later term is its universality: it does not depend on the graph Γ, but only on the zeros of P on the unit torus and on an explicit (purely imaginary) shape parameter. A similar expansion is also obtained in the non-bipartite case, assuming a conjectural condition on the zeros of P. We then show that this asymptotic expansion holds for the Ising partition function as well, with fsc taking a particularly simple form: it vanishes in the subcritical regime, is equal to log(2) in the supercritical regime, and to an explicit function of the shape parameter at criticality. These results are in full agreement with the conformal field theory predictions of Blöte, Cardy and Nightingale. [ABSTRACT FROM AUTHOR]

Purpose: 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. [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]

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]

Conventional gas–liquid phase transitions feature a coexistence line that has a monotonic and positive slope in line with our intuition that cooling always leads to condensation. Here, we study the inverse phenomenon, condensation of adsorbed organic molecules into dense domains upon heating. Our considerations are motivated by recent experiments [Aeschlimann et al., Angew. Chem., Int. Ed. 60, 19117–19122 (2021)], which demonstrate the partial dissolution of an ordered molecular monolayer and the mobilization of molecules upon cooling. We introduce a simple lattice model in which each site can have three states corresponding to unoccupied and two discernible molecular conformations. We investigate this model through Monte Carlo simulations, mean-field theory, and exact results based on the analytical solution of the Ising model in two dimensions. Our results should be broadly applicable to molecules with distinct conformations that have sufficiently different entropies or heat capacities. [ABSTRACT FROM AUTHOR]

Generally, Co-based Heusler alloys are the center of interest because of their properties such as high Curie temperature, spin polarization, and high value of exchange bias. Herein, we have used the macroscopic technique to probe the low-temperature exotic properties of M1.5Co0.5FeAl. First, we have analyzed the dc magnetization data, and it unfolds the presence of a glassy phase at 33 K. The cluster spin glass phase is authenticated by measuring ac susceptibility. Furthermore, using empirical models like power law and Vogel–Fulcher fitting, the relaxation time for the spin is of the order of τ ∼ 10−9 s, confirming the presence of a cluster spin glass in Mn1.5Co0.5FeAl below an irreversible temperature. The H–T phase space diagram ensures that it follows the Ising spin model. Furthermore, the glassy phase of the system is confirmed by magnetic relaxation, memory effect, and the presence of an exchange bias instead of a minor loop below spin-freezing temperature (Tf ∼ 33 K). [ABSTRACT FROM AUTHOR]

In this current investigation, we have carefully studied the structural, magnetic, magnetocaloric effect and the critical phenomena of the La0.7Ba0.3−xMn0.95Fe0.05O3(x = 0 and 0.06) compounds. The structural study pinpoints that the best structure for the compounds crystallization is the rhombohedral structure with the symmetry of R-3C. The M (T) curves indicated that the compounds exhibit a magnetic transition from the ferromagnetic coupling to the paramagnetic coupling around the Curie temperature Tc. The calculation of Tc with the derivative method gives these values: Tc = 263 ± 0.5 K and 238 ± 0.5 K for x = 0 and x = 0.06, respectively. We showed that the experimental effective moment is higher than the theoretical thanks to the presence of some ferromagnetic coupling in the paramagnetic state. The magnetic entropy change as a function of temperature displayed the transition from order to disorder state around the Curie temperature Tc. The several values of −ΔSM at 5 T applied magnetic field is equal to 2.9 ± 0.1 J/Kg K and 2.1 ± 0.1 J/Kg K for x = 0 and 0.06, respectively. One can deduce that our compounds can be as perfect candidates in the magnetic refrigeration especially the parent compound due to the Curie temperature is around to the room temperature. The universal master curves showed that the compound displayed a second order magnetic transition. In the aim to identify the universality class, we turn to study the critical phenomena. Based on Banerjee approach, we confirm again that the compounds exhibit a second order transition. Following the mean field approximation, we determined that the Ising model is the best for the undoped compound and when the barium content decreases, the model would be the tricritical mean field model. We determined the several values of the critical exponents and we showed that are so close to of the theoretical model chosen. We confirm the reliability of the determined exponent values through the scaling theory. [ABSTRACT FROM AUTHOR]

The suppression of ferroquadrupolar order in TmVO4 in a magnetic field is well-described by the transverse field Ising model, enabling detailed studies of critical dynamics near the quantum phase transition. We describe nuclear magnetic resonance measurements in pure and Y-doped single crystals. The non-Kramers nature of the ground state doublet leads to a unique form of the hyperfine coupling that exclusively probes the transverse field susceptibility. Our results show that this quantity diverges at the critical field, in contrast to the mean-field prediction. Furthermore, we find evidence for quantum critical fluctuations present near Tm-rich regions in Y-doped crystals at levels beyond which long-range order is suppressed, suggesting the presence of quantum Griffiths phases. [ABSTRACT FROM AUTHOR]

The equilibrium and phase properties of the Ising model with three-spin interaction and an external field are studied within the framework of mean-field approximation. The thermodynamic properties of the model reveals two coexistence curves, signifying two distinct second-order phase transitions, dependent on the domain of the interaction parameter. The critical exponents of the magnetic order parameter are calculated in all directions of the phase space and show their agreement with the mean-field universality class. [ABSTRACT FROM AUTHOR]