Search

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]

We study spin models on Euclidean black hole backgrounds. These resemble the Ising model, but are inhomogeneous with two parameters, the black hole mass and the cosmological constant. We use Monte-Carlo methods to study macroscopic properties of these systems for Schwarzschild and anti-deSitter black holes in four and five dimensions for spin-1/2 and spin-1. We find in every case that increasing the black hole mass causes the spins to undergo a second order phase transition from disorder to order and that the phase transition occurs at sub-Planckian black hole mass. [ABSTRACT FROM AUTHOR]

We derive exact finite-size corrections for the free energy F of the Ising model on the square lattice with Brascamp–Kunz boundary conditions. We calculate ratios r p (ρ) of p th coefficients of F for the infinitely long cylinder () and the infinitely long Brascamp–Kunz strip () at varying values of the aspect ratio . Like previous studies have shown for the two-dimensional dimer model, the limiting values p → ∞ of r p (ρ) exhibit abrupt anomalous behavior at certain values of ρ. These critical values of ρ and the limiting values of the finite-size-expansion-coefficient ratios differ, however, between the two models. [ABSTRACT FROM AUTHOR]

We consider torsion in parameter manifolds that arises via conformal transformations of the Fisher information metric, and define it for information geometry of a wide class of physical systems. The torsion can be used to differentiate between probability distribution functions that otherwise have the same scalar curvature and hence define similar geometries. In the context of thermodynamic geometry, our construction gives rise to a new scalar—the torsion scalar defined on the manifold, while retaining known physical features related to other scalar quantities. We analyse this in the context of the Van der Waals and the Curie–Weiss models. In both cases, the torsion scalar has non trivial behaviour on the spinodal curve. We also briefly comment on the one dimensional classical Ising model and show that the torsion scalar diverges exponentially near criticality. [ABSTRACT FROM AUTHOR]

Comprehensive studies are made on the six-state clock universality of two models using several approaches. We apply the machine-learning technique of phase classification to the antiferromagnetic (AF) three-state Potts model on the square lattice with ferromagnetic next-nearest-neighbor (NNN) coupling and the triangular AF Ising model with anisotropic NNN coupling to study two Berezinskii–Kosterlitz–Thouless transitions. We also use the Monte Carlo simulation paying attention to the ratio of correlation functions of different distances for these two models. The obtained results are compared with those of the previous studies using the level-spectroscopy method. We directly show the six-state clock universality for totally different systems with the machine-learning study. [ABSTRACT FROM AUTHOR]

Quantum phase transitions with multicritical points are fascinating phenomena occurring in interacting quantum many-body systems. However, multicritical points predicted by theory have been rarely verified experimentally; finding multicritical points with specific behaviors and realizing their control remains a challenging topic. Here, we propose a system that a quantized light field interacts with a two-level atomic ensemble coupled by microwave fields in optical cavities, which is described by a generalized Dicke model. Multicritical points for the superradiant quantum phase transition are shown to occur. We determine the number and position of these critical points and demonstrate that they can be effectively manipulated through the tuning of system parameters. Particularly, we find that the quantum critical points can evolve into a Lifshitz point (LP) if the Rabi frequency of the light field is modulated periodically in time. Remarkably, the texture of atomic pseudo-spins can be used to characterize the quantum critical behaviors of the system. The magnetic orders of the three phases around the LP, represented by the atomic pseudo-spins, are similar to those of an axial next-nearest-neighboring Ising model. The results reported here are beneficial for unveiling intriguing physics of quantum phase transitions and pave the way towards to find novel quantum multicritical phenomena based on the generalized Dicke model. [ABSTRACT FROM AUTHOR]

The Ising model with a transverse field and an antiferromagnetic transverse interaction is represented as a matrix in the computational basis with non-zero off-diagonal elements with both positive and negative signs and thus may be regarded to be non-stoquastic. We show that the local Boltzmann factors of such a system under an appropriate Suzuki–Trotter representation can be chosen non-negative and thus may potentially be simulated classically without a sign problem if the parameter values are limited to a subspace of the whole parameter space. We then derive conditions for parameters to satisfy asymptotically in order that simulated quantum annealing of this system converges to thermal equilibrium in the long-time limit. [ABSTRACT FROM AUTHOR]

We investigate the Ising and Heisenberg models using the block renormalization group method (BRGM), focusing on its behavior across different system sizes. The BRGM reduces the number of spins by a factor of 1/2 (1/3) for the Ising (Heisenberg) model, effectively preserving essential physical features of the model while using only a fraction of the spins. Through a comparative analysis, we demonstrate that as the system size increases, there is an exponential convergence between results obtained from the original and renormalized Ising Hamiltonians, provided the coupling constants are redefined accordingly. Remarkably, for a spin chain with 24 spins, all physical features, including magnetization, correlation function, and entanglement entropy, exhibit an exact correspondence with the results from the original Hamiltonian. The study of the Heisenberg model also shows this tendency, although complete convergence may appear for a size much larger than 24 spins, and is therefore beyond our computational capabilities. The success of BRGM in accurately characterizing the Ising model, even with a relatively small number of spins, underscores its robustness and utility in studying complex physical systems, and facilitates its simulation on current NISQ computers, where the available number of qubits is largely constrained.

All standard measures of bipartite entanglement in one-dimensional quantum field theories can be expressed in terms of correlators of branch point twist fields, here denoted by and . These are symmetry fields associated to cyclic permutation symmetry in a replica theory and having the smallest conformal dimension at the critical point. Recently, other twist fields (composite twist fields), typically of higher dimension, have been shown to play a role in the study of a new measure of entanglement known as the symmetry resolved entanglement entropy. In this paper we give an exact expression for the two-point function of a composite twist field that arises in the Ising field theory. In doing so we extend the techniques originally developed for the standard branch point twist field in free theories as well as an existing computation due to Horváth and Calabrese of the same two-point function which focused on the leading large-distance contribution. We study the ground state two-point function of the composite twist field and its conjugate . At criticality, this field can be defined as the leading field in the operator product expansion of and the disorder field µ. We find a general formula for log 〈 T μ (0) T μ † (r) 〉 and for (the derivative of) its analytic continuation to positive real replica numbers greater than 1. We check our formula for consistency by showing that at short distances it exactly reproduces the expected conformal dimension. [ABSTRACT FROM AUTHOR]

We study a nonequilibrium mean field Ising model in the low temperature phase regime, where metastable equilibrium states develop a cuspidal (spinodal) singularity. We focus on celebrated Glauber dynamics, and design a contact Hamiltonian flow which captures some of its rough features in this regime. We prove, however, that there is an inevitable discrepancy between the scaling laws for the relaxation time in the Glauber and the contact Hamiltonian dynamical systems. [ABSTRACT FROM AUTHOR]

Complex models in physics, biology, economics, and engineering are often sloppy, meaning that the model parameters are not well determined by the model predictions for collective behavior. Many parameter combinations can vary over decades without significant changes in the predictions. This review uses information geometry to explore sloppiness and its deep relation to emergent theories. We introduce the model manifold of predictions, whose coordinates are the model parameters. Its hyperribbon structure explains why only a few parameter combinations matter for the behavior. We review recent rigorous results that connect the hierarchy of hyperribbon widths to approximation theory, and to the smoothness of model predictions under changes of the control variables. We discuss recent geodesic methods to find simpler models on nearby boundaries of the model manifold—emergent theories with fewer parameters that explain the behavior equally well. We discuss a Bayesian prior which optimizes the mutual information between model parameters and experimental data, naturally favoring points on the emergent boundary theories and thus simpler models. We introduce a 'projected maximum likelihood' prior that efficiently approximates this optimal prior, and contrast both to the poor behavior of the traditional Jeffreys prior. We discuss the way the renormalization group coarse-graining in statistical mechanics introduces a flow of the model manifold, and connect stiff and sloppy directions along the model manifold with relevant and irrelevant eigendirections of the renormalization group. Finally, we discuss recently developed 'intensive' embedding methods, allowing one to visualize the predictions of arbitrary probabilistic models as low-dimensional projections of an isometric embedding, and illustrate our method by generating the model manifold of the Ising model. [ABSTRACT FROM AUTHOR]

We revisit, with a pedagogical heuristic motivation, the lambda extension of the low-temperature row correlation functions C (M , N) of the two-dimensional Ising model. In particular, using these one-parameter series to understand the deformation theory around selected values of λ , namely λ = cos (π m / n) with m and n integers, we show that these series yield perturbation coefficients, generalizing form factors, that are D-finite functions. As a by-product these exact results provide an infinite number of highly non-trivial identities on the complete elliptic integrals of the first and second kind. These results underline the fundamental role of Jacobi theta functions and Jacobi forms, the previous D-finite functions being (relatively simple) rational functions of Jacobi theta functions, when rewritten in terms of the nome of elliptic functions. [ABSTRACT FROM AUTHOR]

We revisit the Haakeâ€"Lewensteinâ€"Wilkens approach to Edwardsâ€"Anderson (EA) model of Ising spin glass (SG) (Haake et al 1985 Phys. Rev. Lett. 55 2606). This approach consists in evaluation and analysis of the probability distribution of configurations of two replicas of the system, averaged over quenched disorder. This probability distribution generates squares of thermal copies of spin variables from the two copies of the systems, averaged over disorder, that is the terms that enter the standard definition of the original EA order parameter, q EA . We use saddle point/steepest descent (SPSD) method to calculate the average of the Gaussian disorder in higher dimensions. This approximate result suggest that q EA > 0 at 0 < T < T c in 3D and 4D. The case of 2D seems to be a little more subtle, since in the present approach energy increase for a domain wall competes with boundary/edge effects more strongly in 2D; still our approach predicts SG order at sufficiently low temperature. We speculate, how these predictions confirm/contradict widely spread opinions that: (i) There exist only one (up to the spin flip) ground state in EA model in 2D, 3D and 4D; (ii) there is (no) SG transition in 3D and 4D (2D). This paper is dedicated to the memories of Fritz Haake and Marek Cieplak. [ABSTRACT FROM AUTHOR]

The Fisher zeros of the Baxterâ€"Wu model are examined for the first time and for two series of finite-sized systems, with ‘spherical’ boundary conditions, their location is found to be extremely simple. They lie on the unit circle in the complex sinh[2 βJ 3] plane. This is the same location as the Fisher zeros of the square lattice Ising model with nearest neighbour interactions and Brascampâ€"Kunz boundary conditions. The Baxterâ€"Wu model is an Ising model with three-site interactions, J 3, on the triangle lattice. From the leading Fisher zeros, using finite-size scaling, accurate estimates of the critical exponent 1/ ν are obtained and emphasis is placed on using different variables such as exp[âˆ'2 βJ 3], exp[âˆ'4 βJ 3], and sinh[2 βJ 3] to enhance the accuracy of estimates. Furthermore, using the imaginary parts of the leading zeros versus the real part of the leading zeros, yields different results. This is similar to results of Janke and Kenna for the nearest neighbour, Ising model on the square lattice and extends this behaviour to a multisite interaction system in a different universality class than the pair-interaction cases. [ABSTRACT FROM AUTHOR]

Using an effective field theory with correlations, magnetic properties of an octahedral chain described by a mixed spin Ising model are investigated. Unique phenomena such as multiple hysteresis loops, saturation magnetization, and reverse flip of the magnetization plateaus occur when certain typical parameters are applied. These results may be helpful to further investigate the magnetic properties of one-dimensional systems and could potentially be utilized in the design of spin devices. [ABSTRACT FROM AUTHOR]

The upper critical dimension of the Ising model is known to be d c = 4, above which critical behavior is regarded to be trivial. We hereby argue from extensive simulations that, in the random-cluster representation, the Ising model simultaneously exhibits two upper critical dimensions at (d c = 4, d p = 6), and critical clusters for d ≥ d p, except the largest one, are governed by exponents from percolation universality. We predict a rich variety of geometric properties and then provide strong evidence in dimensions from 4 to 7 and on complete graphs. Our findings significantly advance the understanding of the Ising model, which is a fundamental system in many branches of physics. [ABSTRACT FROM AUTHOR]

We discuss how to calculate non-equilibrium universal amplitude ratios in the functional renormalization group approach, extending its applicability. In particular, we focus on the critical relaxation of the Ising model with non-conserved dynamics (model A) and calculate the universal amplitude ratio associated with the fluctuationâ€"dissipation ratio of the order parameter, considering a critical quench from a high-temperature initial condition. Our predictions turn out to be in good agreement with previous perturbative renormalization-group calculations and Monte Carlo simulations. [ABSTRACT FROM AUTHOR]

We investigate quantum phase transitions for q -state quantum Potts models (q = 2,3,4) on a square lattice and for the Ising model on a honeycomb lattice by using the infinite projected entangled-pair state algorithm with a simplified updating scheme. We extend the universal order parameter to a two-dimensional lattice system, which allows us to explore quantum phase transitions with symmetry-broken order for any translation-invariant quantum lattice system of the symmetry group G. The universal order parameter is zero in the symmetric phase, and it ranges from zero to unity in the symmetry-broken phase. The ground-state fidelity per lattice site is computed, and a pinch point is identified on the fidelity surface near the critical point. The results offer another example highlighting the connection between (i) critical points for a quantum many-body system undergoing a quantum phase-transition and (ii) pinch points on a fidelity surface. In addition, we discuss three quantum coherence measures: the quantum Jensenâ€"Shannon divergence, the relative entropy of coherence, and the l1 norm of coherence, which are singular at the critical point, thereby identifying quantum phase transitions. [ABSTRACT FROM AUTHOR]

Majorana-based quantum gates are not complete for performing universal topological quantum computation while Fibonacci-based gates are difficult to be realized electronically and hardly coincide with the conventional quantum circuit models. In reference Hu and Kane (2018 Phys. Rev. Lett. 120 066801), it has been shown that a strongly correlated Majorana edge mode in a chiral topological superconductor can be decomposed into a Fibonacci anyon τ and a thermal operator anyon ɛ in the tricritical Ising model. The deconfinement of τ and ɛ via the interaction between the fermion modes yields the anyon collisions and gives the braiding of either τ or ɛ. With these braidings, the complete members of a set of universal gates, the Pauli gates, the Hadamard gate and extra phase gates for one-qubit as well as controlled-NOT (CNOT) gate for two-qubits, are topologically assembled. Encoding quantum information and reading out the computation results can be carried out through electric signals. With the sparse-dense mixed encodings, we set up the quantum circuit where the CNOT gate turns out to be a probabilistic gate and design the corresponding devices with thin films of the chiral topological superconductor. As an example of the universal topological quantum computing, we show the application to Shor’s integer factorization algorithm. [ABSTRACT FROM AUTHOR]

We investigate the problem of minimizing the entropy production for a physical process that can be described in terms of a Markov jump dynamics. We show that, without any further constraints, a given time-evolution may be realized at arbitrarily small entropy production, yet at the expense of diverging activity. For a fixed activity, we find that the dynamics that minimizes the entropy production is driven by conservative forces. The value of the minimum entropy production is expressed in terms of the graph-distance based Wasserstein distance between the initial and final configuration. This yields a new kind of speed limit relating dissipation, the average number of transitions and the Wasserstein distance. It also allows us to formulate the optimal transport problem on a graph via continuous-time interpolating dynamics, in complete analogy to the continuous space setting. We demonstrate our findings for simple state networks, a time-dependent pump and for spin flips in the Ising model. [ABSTRACT FROM AUTHOR]

Gibbs sampling is fundamental to a wide range of computer algorithms. Such algorithms are set to be replaced by physics based processors—be it quantum or stochastic annealing devices—which embed problem instances and evolve a physical system into a low-energy ensemble to recover a probability distribution. At a critical constraint to variable ratio, satisfiability (SAT) problem instances exhibit a SAT-UNSAT transition (frustrated to frustration free). Algorithms require increasing computational resources from this critical point. This is a so called, algorithmic or computational phase transition and has extensively been studied. In this paper we consider the complexity in sampling and recovering ground states from resultant distributions of a physics based processor. In particular, we first consider the ideal Gibbs distributions at some fixed inverse temperature and observe that the success probability in sampling and recovering ground states decrease for instances starting at the critical density. Furthermore, simulating the Gibbs distribution, we employ Ising spin dynamics, which play a crucial role in understanding of non-equilibrium statistical physics, to find their steady states of 2-SAT Hamiltonians. We observe that beyond the critical density, the probability of sampling ground states decreases. Our results apply to several contemporary devices and provide a means to experimentally probe a signature of the computational phase transition.

Deforestation is a prominent example of anthropogenic land change. Here we investigate deforestation from a landscape ecology perspective by process-based modeling of a sequence of consecutive landscape patterns starting from a homogeneous forest and ending in homogeneous agricultural land. We propose an Ising-like neutral model to mimic the deforestation dynamics. Our goal is to demonstrate that such a simple conceptualization of the deforestation process is capable of simulating an evolutionary sequence of landscape patterns matching empirical data. The model has only two parameters, one representing an external pressure (for or against deforestation), and another representing a propensity of land for spatial autocorrelation. We perform a suite of simulations to link a process, as parameterized by the values of the two parameters, to the sequence of landscape patterns. We have found a narrow range of parameters for which the model quantitatively and visually matches empirical data. This indicates that the Ising-like neutral model captures the essential aspects of a deforestation process and that the temporal sequence of intermediate landscape patterns does not depend on the details of the process.

The solutions of the problems related to open quantum systems have attracted considerable interest. We propose a variational quantum algorithm to find the steady state of open quantum systems. In this algorithm, we employ parameterized quantum circuits to prepare the purification of the steady state and define the cost function based on the Lindblad master equation, which can be efficiently evaluated with quantum circuits. We then optimize the parameters of the quantum circuit to find the steady state. Numerical simulations are performed on the one-dimensional transverse field Ising model with dissipative channels. The result shows that the fidelity between the optimal mixed state and the true steady state is over 99%. This algorithm is derived from the natural idea of expressing mixed states with purification and it provides a reference for the study of open quantum systems. [ABSTRACT FROM AUTHOR]

The 2d orders are a sub class of causal sets, which is especially amenable to computer simulations. Past work has shown that the 2d orders have a first order phase transition between a random and a crystalline phase. When coupling the 2d orders to the Ising model, this phase transition coincides with the transition of the Ising model. The coupled system also shows a new phase, at negative β, where the Ising model induces the geometric transition. In this article we examine the phase transitions of the coupled system, to determine their order, as well as how they scale when the system size is changed. We find that the transition at positive β seems to be of mixed order, while the two transitions at negative β appear continuous/first order for the Ising model/the geometry respectively. The scaling of the observables with the system size on the other hand is fairly simple, and does, where applicable, agree with that found for the pure 2d orders. We find that the location of these transitions has fractional scaling in the system size. [ABSTRACT FROM AUTHOR]

Manganites La0.93K0.07Mn1−xCuxO3 prepared by the solid state reaction method at high temperature, were studied structurally and magnetically. The unit cell parameters, as well as bond length and the bond angle , were determined from the Rietveld refinement of the x-ray diffraction patterns. The Fourier-transform infrared spectroscopy analysis shows that Cu2+ substitution induces variations in the vibration modes of the MnO6 octahedra. Magnetization vs. temperature at low magnetic field were performed in the range under field coolingand zero field cooling conditions. All the samples exhibited a second-order paramagnetic–ferromagnetic (FM) transition at Curie temperature, , in the range between 199 and 285 K. The inverse susceptibility, exhibits a linear Curie-Weiss (C-W) behavior for , while for , it shows a deviation from the linear behavior predicted by the Heisenberg model. The mentioned deviation of means that a short ferromagnetic state formation is present even for , which were characterized by the experimental effective magnetic moment, A null spontaneous magnetization, above was evaluated for all samples by using the Kouvel-Fisher method. This work evaluates the short-range FM clusters by means of an extension of the C-W approach to the region, i.e.,. Finally, the critical coefficient values, and , showed that the 3D Heisenberg model fits adequately the and samples, while the 3D Ising model fits the sample. [ABSTRACT FROM AUTHOR]

Time evolution and scattering simulation in phenomenological models are of great interest for testing and validating the potential for near-term quantum computers to simulate quantum field theories. Here, we simulate one-particle propagation and two-particle scattering in the one-dimensional transverse Ising model for 3 and 4 spatial sites with periodic boundary conditions on a quantum computer. We use the quantum Lanczos algorithm to obtain all energy levels and corresponding eigenstates of the system. We simplify the quantum computation by taking advantage of the symmetries of the system. These results enable us to compute one- and two-particle transition amplitudes, particle numbers for spatial sites, and the transverse magnetization as functions of time. The quantum circuits were executed on various IBM Q superconducting hardware. The experimental results are in very good agreement with the values obtained using exact diagonalization. [ABSTRACT FROM AUTHOR]

The ability to tune and control the magnetic phases of two-dimensional (2D) nanomagnets at room temperature is indispensable for the development of future spintronics and low-dimensional spin circuits. In this work, a first-principles-based investigation combined with a Monte Carlo simulation based on a 2D Ising model is used to investigate the electronic and magnetic behaviour of a recently discovered 2D material, Cr2Ge2Se6 over a large range of strain and electric field strength. This material offers ferromagnetic antiferromagnetic and semiconductor metallic phase transitions in different regimes. In the presence of strain, a colossal enhancement of the critical temperature (Tc) is observed, from 149 K to 885 K. The application of an electric field allows a further enhancement of the Tc to a value of 919 K, offering a supreme enhancement (~517%), compared to its natural condition. The origin of this behavior can be traced to a super-exchange interaction between the Cr and Se atoms and the intrinsic magnetic anisotropy of Cr2Ge2Se6. The presence of external stimuli engenders spontaneous symmetry breaking with an enhanced magnetic moment (~4.36 /Cr atom), a significant intrinsic spin polarisation (~100%) in a half-metallic regime, and a very high critical temperature. The insights of the current investigation could be useful for future developments in multi-stimuli-assisted room-temperature ferromagnetism and electronic phase control, which are of great significance for future magneto-electronic applications. [ABSTRACT FROM AUTHOR]

The double perovskite Ca2CrSbO6 exhibits a ferromagnetic long-range order below Tc = 13 K and a saturation magnetization of 2.35 μB at 2 K. In this study, the polycrystalline Ca2CrSbO6 is synthesized under high pressure and high temperature, and the critical behavior of the ferromagnetic material as well as the effects of the magnetic behavior due to the isovalent substitution of Sr2+ for Ca2+ is investigated. Also studied are the ferromagnetic criticality of the double perovskite Ca2CrSbO6 at the ferromagnetic transition temperature Tc ≈ 12.6 K from the isotherms of magnetization M(H) via an iteration process and the Kouvel–Fisher method. The critical exponents associated with the transition are determined as follows: β = 0.322, γ = 1.241, and δ = 4.84. The magnetization data in the vicinity of Tc can be scaled into two universal curves in the plot of M/| ε |βversusH/| ε |β + γ, where ε = T/Tc – 1. The obtained β and γ values are consistent with the predicted values from a three-dimensional Ising model. The effects of Sr substitution on the double perovskite Ca2CrSbO6 are taken into consideration. As the Sr content increases, the (Ca2 – xSrx)CrSbO6 polycrystal shows a continuous switch from ferromagnetic to antiferromagnetic behavior. [ABSTRACT FROM AUTHOR]

The double perovskite Ca2CrSbO6 exhibits a ferromagnetic long-range order below Tc = 13 K and a saturation magnetization of 2.35 μB at 2 K. In this study, the polycrystalline Ca2CrSbO6 is synthesized under high pressure and high temperature, and the critical behavior of the ferromagnetic material as well as the effects of the magnetic behavior due to the isovalent substitution of Sr2+ for Ca2+ is investigated. Also studied are the ferromagnetic criticality of the double perovskite Ca2CrSbO6 at the ferromagnetic transition temperature Tc ≈ 12.6 K from the isotherms of magnetization M(H) via an iteration process and the Kouvel–Fisher method. The critical exponents associated with the transition are determined as follows: β = 0.322, γ = 1.241, and δ = 4.84. The magnetization data in the vicinity of Tc can be scaled into two universal curves in the plot of M/| ε |βversusH/| ε |β + γ, where ε = T/Tc – 1. The obtained β and γ values are consistent with the predicted values from a three-dimensional Ising model. The effects of Sr substitution on the double perovskite Ca2CrSbO6 are taken into consideration. As the Sr content increases, the (Ca2 – xSrx)CrSbO6 polycrystal shows a continuous switch from ferromagnetic to antiferromagnetic behavior. [ABSTRACT FROM AUTHOR]

The dynamic phase transition properties for ferroelectric nanotube under a spin-1/2 transverse Ising model are studied under the effective field theory (EFT) with correlations. The temperature effects on the pseudo-spin systems are unveiled in three-dimensional (3-D) and two-dimensional (2-D) phase diagrams. Moreover, the dynamic behaviors of exchange interactions on the 3-D and 2-D phase transitions under high temperature are exhibited. The results present that it is hard to obtain pure ferroelectric phase under high temperature; that is, the vibration of orderly pseudo-spins cannot be eliminated completely. [ABSTRACT FROM AUTHOR]

Quantum simulation has been developed extensively over the past decades, widely applied to different models to explore dynamics in the quantum regime. Rydberg atoms have strong dipole–dipole interactions and interact with each other over a long distance, which makes it straightforward to build many-body interacting quantum systems to simulate specific models. Additionally, neutral atoms are easily manipulated due to their weak interactions. These advantages make Rydberg many-body system an ideal platform to implement quantum simulations. This paper reviews several quantum simulations for different models based on Rydberg many-body systems, including quantum Ising models in one dimension and two dimensions mainly for quantum magnetism, XY model for excitation transport, SSH model for symmetry-protected topological phases, and critical self-organized behaviors in many-body systems. Besides, some challenges and promising directions of quantum simulations based on Rydberg many-body system are discussed in this paper. [ABSTRACT FROM AUTHOR]

Symmetry breaking plays a pivotal role in modern physics. Although self-similarity is also a symmetry, and appears ubiquitously in nature, a fundamental question arises as to whether self-similarity breaking makes sense or not. Here, by identifying an important type of critical fluctuation, dubbed 'phases fluctuations', and comparing the numerical results for those with self-similarity and those lacking self-similarity with respect to phases fluctuations, we show that self-similarity can indeed be broken, with significant consequences, at least in nonequilibrium situations. We find that the breaking of self-similarity results in new critical exponents, giving rise to a violation of the well-known finite-size scaling, or the less well-known finite-time scaling, and different leading exponents in either the ordered or the disordered phases of the paradigmatic Ising model on two- or three-dimensional finite lattices, when subject to the simplest nonequilibrium driving of linear heating or cooling through its critical point. This is in stark contrast to identical exponents and different amplitudes in usual critical phenomena. Our results demonstrate how surprising driven nonequilibrium critical phenomena can be. The application of this theory to other classical and quantum phase transitions is also anticipated. [ABSTRACT FROM AUTHOR]

We introduce an unsupervised machine learning method based on Siamese neural networks (SNNs) to detect phase boundaries. This method is applied to Monte-Carlo simulations of Ising-type systems and Rydberg atom arrays. In both cases the SNN reveals phase boundaries consistent with prior research. The combination of leveraging the power of feed-forward neural networks, unsupervised learning and the ability to learn about multiple phases without knowing about their existence provides a powerful method to explore new and unknown phases of matter.

Continuous phase transition in quantum matters is a significant issue in condensed matter physics. In general, the continuous quantum phase transitions in many-body systems occur with gap closing. On the other hand, non-Hermitian systems could display quite different properties as their Hermitian counterparts. In this paper, we show that a hidden, continuous quantum phase transition occurs without gap closing in non-Hermitian transverse Ising model. By using a projected Jordan–Wigner transformation, the one-dimensional (1D) non-Hermitian transverse Ising model with ferromagnetic order is mapped on to 1D non-Hermitian Kitaev model with topological superconducting order and becomes exactly solvable. A hidden, continuous quantum phase transition is really normal–abnormal transition for fermionic correlation in the 1D non-Hermitian Kitaev model. In addition, similar hidden, continuous quantum phase transition is discovered in two-dimensional non-Hermitian transverse Ising model and thus becomes a universal feature in certain non-Hermitian many-body systems.

We investigate the transverse field Ising model subject to a two-step periodic driving protocol and quasiperiodic modulation of the Ising couplings. Analytical results on the phase boundaries associated with Majorana edge modes and numerical results on the localization of single-particle excitations are presented. The implication of a region with fully localized domain-wall-like excitations in the parameter space is eigenstate order and exact spectral pairing of Floquet eigenstates, based on which we conclude the existence of time crystals. We also examine various correlation functions of the time crystal phase numerically, in support of its existence. [ABSTRACT FROM AUTHOR]

We continue our analysis of Ising models on the (directed) Erdős–Rényi random graph. This graph is constructed on N vertices and every edge has probability p to be present. These models were introduced and first studied by Bovier and Gayrard (1993 J. Stat. Phys. 72 643–64) and further analyzed by the authors in a previous note, in which we consider the case of p = p(N) satisfying p3N2 → ∞ and β < 1. In the current note we prove a quenched central limit theorem for the magnetization for p satisfying pN → ∞ in the high-temperature regime β < 1. We also show a non-standard central limit theorem for p4N3 → ∞ at the critical temperature β = 1. For p4N3 → 0 we obtain a Gaussian limiting distribution for the magnetization. Finally, in the critical regime p4N3 → c the limiting distribution for the magnetization contains a Gaussian component as well as a -term. Hence, at β = 1 we observe a phase transition in p for the fluctuations of the magnetization. [ABSTRACT FROM AUTHOR]

Determining the phase diagram of systems consisting of smaller subsystems 'connected' via a tunable coupling is a challenging task relevant for a variety of physical settings. A general question is whether new phases, not present in the uncoupled limit, may arise. We use machine learning and a suitable quasidistance between different points of the phase diagram to study layered spin models, in which the spin variables constituting each of the uncoupled systems (to which we refer as layers) are coupled to each other via an interlayer coupling. In such systems, in general, composite order parameters involving spins of different layers may emerge as a consequence of the interlayer coupling. We focus on the layered Ising and Ashkin–Teller models as a paradigmatic case study, determining their phase diagram via the application of a machine learning algorithm to the Monte Carlo data. Remarkably our technique is able to correctly characterize all the system phases also in the case of hidden order parameters, i.e. order parameters whose expression in terms of the microscopic configurations would require additional preprocessing of the data fed to the algorithm. We correctly retrieve the three known phases of the Ashkin–Teller model with ferromagnetic couplings, including the phase described by a composite order parameter. For the bilayer and trilayer Ising models the phases we find are only the ferromagnetic and the paramagnetic ones. Within the approach we introduce, owing to the construction of convolutional neural networks, naturally suitable for layered image-like data with arbitrary number of layers, no preprocessing of the Monte Carlo data is needed, also with regard to its spatial structure. The physical meaning of our results is discussed and compared with analytical data, where available. Yet, the method can be used without any a priori knowledge of the phases one seeks to find and can be applied to other models and structures. [ABSTRACT FROM AUTHOR]

We explore the coherent dynamics in a small network of three coupled parametric oscillators and demonstrate the effect of frustration on the persistent beating between them. Since a single-mode parametric oscillator represents an analogue of a classical Ising spin, networks of coupled parametric oscillators are considered as simulators of Ising spin models, aiming to efficiently calculate the ground state of an Ising network—a computationally hard problem. However, the coherent dynamics of coupled parametric oscillators can be considerably richer than that of Ising spins, depending on the nature of the coupling between them (energy preserving or dissipative), as was recently shown for two coupled parametric oscillators. In particular, when the energy-preserving coupling is dominant, the system displays everlasting coherent beats, transcending the Ising description. Here, we extend these findings to three coupled parametric oscillators, focussing in particular on the effect of frustration of the dissipative coupling. We theoretically analyse the dynamics using coupled nonlinear Mathieu's equations, and corroborate our theoretical findings by a numerical simulation that closely mimics the dynamics of the system in an actual experiment. Our main finding is that frustration drastically modifies the dynamics. While in the absence of frustration the system is analogous to the two-oscillator case, frustration reverses the role of the coupling completely, and beats are found for small energy-preserving couplings. [ABSTRACT FROM AUTHOR]

As a problem in data science the inverse Ising (or Potts) problem is to infer the parameters of a Gibbs–Boltzmann distributions of an Ising (or Potts) model from samples drawn from that distribution. The algorithmic and computational interest stems from the fact that this inference task cannot be carried out efficiently by the maximum likelihood criterion, since the normalizing constant of the distribution (the partition function) cannot be calculated exactly and efficiently. The practical interest on the other hand flows from several outstanding applications, of which the most well known has been predicting spatial contacts in protein structures from tables of homologous protein sequences. Most applications to date have been to data that has been produced by a dynamical process which, as far as it is known, cannot be expected to satisfy detailed balance. There is therefore no a priori reason to expect the distribution to be of the Gibbs–Boltzmann type, and no a priori reason to expect that inverse Ising (or Potts) techniques should yield useful information. In this review we discuss two types of problems where progress nevertheless can be made. We find that depending on model parameters there are phases where, in fact, the distribution is close to Gibbs–Boltzmann distribution, a non-equilibrium nature of the under-lying dynamics notwithstanding. We also discuss the relation between inferred Ising model parameters and parameters of the underlying dynamics. [ABSTRACT FROM AUTHOR]

We develop a package of numerical simulations implemented in MATLAB to solve complex many-body quantum systems. We focus on widely used examples that include the calculation of the magnetization dynamics for the closed and open Ising model, dynamical quantum phase transition in cavity QED arrays, Markovian dynamics for interacting two-level systems, and the non-Markovian dynamics of the pure-dephasing spin-boson model. These examples will be useful for undergraduate and graduate students with a medium or high-level background in MATLAB, and also for researchers interested in numerical studies applied to quantum optics and condensed matter systems. [ABSTRACT FROM AUTHOR]

We provide a stochastic thermodynamic description across scales for N identical units with all-to-all interactions that are driven away from equilibrium by different reservoirs and external forces. We start at the microscopic level with Poisson rates describing transitions between many-body states. We then identify an exact coarse graining leading to a mesoscopic description in terms of Poisson transitions between system occupations. We proceed studying macroscopic fluctuations using the Martin–Siggia–Rose formalism and large deviation theory. In the macroscopic limit (N → ∞), we derive the exact nonlinear (mean-field) rate equation describing the deterministic dynamics of the most likely occupations. We identify the scaling of the energetics and kinetics ensuring thermodynamic consistency (including the detailed fluctuation theorem) across microscopic, mesoscopic and macroscopic scales. The conceptually different nature of the 'Shannon entropy' (and of the ensuing stochastic thermodynamics) at different scales is also outlined. Macroscopic fluctuations are calculated semi-analytically in an out-of-equilibrium Ising model. Our work provides a powerful framework to study thermodynamics of nonequilibrium phase transitions. [ABSTRACT FROM AUTHOR]

We present a theoretical study of the magnetic properties of the lanthanum copper manganate double perovskite La2CuMnO6 ceramic, using Monte Carlo simulations. We analyze and discuss the ground state phase diagrams in different planes to show the effect of every physical parameter. Based on the Monte Carlo simulations, which combine Metropolis algorithm and Ising model, we explore the thermal behavior of the total magnetization and susceptibility. We also present and discuss the influence of physical parameters such as the external magnetic field, the exchange coupling interactions between magnetic atoms, and the exchange magnetic field on the magnetization of the system. Moreover, the critical temperature of the system is about Tc = 70 K, in agreement with the experimental value. Finally, the hysteresis loops of La2CuMnO6 are discussed. [ABSTRACT FROM AUTHOR]

In this article we present a full description of the quantum Kerr Ising model—a linear optical network of parametrically pumped Kerr nonlinearities. We consider the non-dissipative Kerr Ising model and, using variational techniques, show that the energy spectrum is primarily determined by the adjacency matrix in the Ising model and exhibits highly non-classical cat like eigenstates. We then introduce dissipation to give a quantum mechanical treatment of the measurement process based on homodyne detection via the conditional stochastic Schrodinger equation. Finally, we identify a quantum advantage in comparison to the classical analogue for the example of two anti-ferromagnetic cavities. [ABSTRACT FROM AUTHOR]

We study the Lee–Yang zeros of the quantum ferromagnetic Ising bath via the interaction with the two probe spins. Similarly, as in an earlier paper (Wei and Liu 2012 Phys. Rev. Lett. 109 , 185701), the problem of detecting the zeros is reduced to the exploration of the time evolution of the probe spins. As a result, the relation between the Lee–Yang zeros of the bath and correlation functions of the probe system is obtained. Also, we obtain the relation between the Lee–Yang zeros and values of the entanglement of the probe spins. We apply these results to the 1D Ising spin model with nearest-neighbor interaction, which can be prepared on trapped atoms. [ABSTRACT FROM AUTHOR]

We derive the exact expression for the Uhlmann fidelity between arbitrary thermal Gibbs states of the quantum XY model in a transverse field with finite system size. Using it, we conduct a thorough analysis of the fidelity susceptibility of thermal states for the Ising model in a transverse field. We compare the exact results with a common approximation that considers only the positive-parity subspace, which is shown to be valid only at high temperatures. The proper inclusion of the odd parity subspace leads to the enhancement of maximal fidelity susceptibility in the intermediate range of temperatures. We show that this enhancement persists in the thermodynamic limit and scales quadratically with the system size. The correct low-temperature behavior is captured by an approximation involving the two lowest many-body energy eigenstates, from which simple expressions are obtained for the thermal susceptibility and specific heat.

Time evolution and scattering simulation in phenomenological models are of great interest for testing and validating the potential for near-term quantum computers to simulate quantum field theories. Here, we simulate one-particle propagation and two-particle scattering in the one-dimensional transverse Ising model for 3 and 4 spatial sites with periodic boundary conditions on a quantum computer. We use the quantum Lanczos algorithm to obtain all energy levels and corresponding eigenstates of the system. We simplify the quantum computation by taking advantage of the symmetries of the system. These results enable us to compute one- and two-particle transition amplitudes, particle numbers for spatial sites, and the transverse magnetization as functions of time. The quantum circuits were executed on various IBM Q superconducting hardware. The experimental results are in very good agreement with the values obtained using exact diagonalization.

In this article we present a full description of the quantum Kerr Ising model—a linear optical network of parametrically pumped Kerr nonlinearities. We consider the non-dissipative Kerr Ising model and, using variational techniques, show that the energy spectrum is primarily determined by the adjacency matrix in the Ising model and exhibits highly non-classical cat like eigenstates. We then introduce dissipation to give a quantum mechanical treatment of the measurement process based on homodyne detection via the conditional stochastic Schrodinger equation. Finally, we identify a quantum advantage in comparison to the classical analogue for the example of two anti-ferromagnetic cavities.

Perhaps the most iconic feature of melting Arctic sea ice is the distinctive ponds that form on its surface. The geometrical patterns describing how melt water is distributed over the surface largely determine the solar reflectance and transmittance of the sea ice cover, which are key parameters in climate modeling and upper ocean ecology. In order to help develop a predictive theoretical approach to studying melting sea ice, and the resulting patterns of light and dark regions on its surface in particular, we look to the statistical mechanics of phase transitions and introduce a two-dimensional random field Ising model which accounts for only the most basic physics in the system. The ponds are identified as metastable states in the model, where the binary spin variable corresponds to the presence of melt water or ice on the sea ice surface. With the lattice spacing determined by snow topography data as the only measured parameter input into the model, energy minimization drives the system toward realistic pond configurations from an initially random state. The model captures the essential mechanism of pattern formation of Arctic melt ponds, with predictions that agree very closely with observed scaling of pond sizes and transition in pond fractal dimension.

Weinvestigate an extension of the quantum Ising (QI) model in one spatial dimension including long-range 1/rα interactions in its statics and dynamicswith possible applications fromheteronuclear polar molecules in optical lattices to trapped ions described by two-state spin systems. We introduce the statics of the system via both numerical techniques with finite size and infinite size matrix product states (MPSs) and a theoretical approaches using a truncated Jordan-Wigner transformation for the ferromagnetic and antiferromagnetic case and show that finite size effects have a crucial role shifting the quantum critical point of the external field by fifteen percent between thirty-two and around fivehundred spins. We numerically study the Kibble-Zurek hypothesis in the long-range QI model with MPSs. A linear quench of the external field through the quantum critical point yields a power-law scaling of the defect density as a function of the total quench time. For example, the increase of the defect density is slower for longer-range models and the critical exponent changes by twenty-five percent. Our study emphasizes the importance of such long-range interactions in statics and dynamics that could point to similar phenomena in a different setup of dynamical systems or for other models. [ABSTRACT FROM AUTHOR]

Instantaneous quantum polynomial-time (IQP) computation is a class of quantum computation consisting only of commuting two-qubit gates and is not universal. Nevertheless, it has been shown that if there is a classical algorithm that can simulate IQP efficiently, the polynomial hierarchy collapses to the third level, which is highly implausible. However, the origin of the classical intractability is still less understood. Here we establish a relationship between IQP and computational complexity of calculating the imaginary-valued partition functions of Ising models. Weapply the established relationship in two opposite directions. One direction is to find subclasses of IQP that are classically efficiently simulatable by using exact solvability of certain types of Ising models. Another direction is applying quantum computational complexity of IQP to investigate (im)possibility of efficient classical approximations of Ising partition functions with imaginary coupling constants. Specifically, we show that a multiplicative approximation of Ising partition functions is#P-hard for almost all imaginary coupling constants even on planar lattices of a bounded degree. [ABSTRACT FROM AUTHOR]