Universality Class Of Ising Model Research Articles

Ordering kinetics with long-range interactions: interpolating between voter and Ising models

Abstract We study the ordering kinetics of a generalization of the voter model with long-range interactions, the p-voter model, in one dimension. It is defined in terms of Boolean variables S i , agents or spins, located on sites i of a lattice, each of which takes in an elementary move the state of the majority of p other agents at distances r chosen with probability P ( r ) ∝ r − α . For p = 2 the model can be exactly mapped onto the case with p = 1, which amounts to the voter model with long-range interactions decaying algebraically. For 3 ⩽ p < ∞ , instead, the dynamics falls into the universality class of the one-dimensional Ising model with long-ranged coupling constant J ( r ) = P ( r ) quenched to small finite temperatures. In the limit p → ∞ , a crossover to the (different) behavior of the long-range Ising model quenched to zero temperature is observed. Since for p > 3 a closed set of differential equations cannot be found, we employed numerical simulations to address this case.

Phase Transition in the Galam’s Majority-Rule Model with Information-Mediated Independence

We study the Galam’s majority-rule model in the presence of an independent behavior that can be driven intrinsically or can be mediated by information regarding the collective opinion of the whole population. We first apply the mean-field approach where we obtained an explicit time-dependent solution for the order parameter of the model. We complement our results with Monte Carlo simulations where our findings indicate that independent opinion leads to order–disorder continuous nonequilibrium phase transitions. Finite-size scaling analysis show that the model belongs to the mean-field Ising model universality class. Moreover, results from an approach with the Kramers–Moyal coefficients provide insights about the social volatility.

Revising the universality class of the four-dimensional Ising model

The aim of this paper is to determine the behavior of the specific heat of the 4-dimensional Ising model in a region around the critical temperature, and via that determine if the Ising model and the ϕ4-model belong to the same universality class in dimension 4. In order to do this we have carried out what is currently the largest scale simulations of the 4-dimensional Ising model, extending the lattices size up to L=256 and the number of samples per size by several orders of magnitude compared to earlier works, keeping track of data for both the canonical and microcanonical ensembles.Our conclusion is that the Ising model has a bounded specific heat, while the ϕ4-model is known to have a logarithmic divergence at the critical point. Hence the two models belong to distinct universality classes in dimension 4.

H-T magnetic phase diagram of CuCrO2: A Monte Carlo study based on a realistic 3D classical Heisenberg model

In the multiferroic geometrically frustrated triangular antiferromagnet CuCrO2, we investigate the magnetic phases as function of temperature under a magnetic field 70 T ≤ B ≤ 120 T along the [001] axis using the importance sampling Monte Carlo method. We consider a realistic three-dimensional classical Heisenberg model, which takes into consideration the distortion and exchange interactions up to the third-nearest neighbors in the ab planes and an interplane interaction, in addition to hard and easy anisotropy axes along the [110] and the [001] directions, respectively. For 70 T ≤ B < 106 T, our calculations show that two phase transitions occur when decreasing the temperature. The first one, which takes place around 30 K, is a “paramagnetic ↔ up-up-down (UUD)” transition and the second one, at lower temperatures, is an “UUD ↔ commensurate Y (CY)” transition. Thus, the colinear UUD phase is stable in an intermediate temperature range. For B = 90 T, our estimates of the critical exponents indicate that the two transitions belong to the universality class of the two-dimensional Ising model. For 106 T ≤ B < 110 T, since the CY phase is identical to the UUD one, only a “paramagnetic ↔ up-up-down (UUD)” transition occurs. For 110 T ≤ B ≤ 120 T, only a “paramagnetic ↔ V” transition is observed at ∼27 K. Our results are in good agreement with the existing experimental data on the stable phases in this magnetic field range. Moreover, we have determined the temperature range where the CY and UUD phases are stable which was not done previously.

Effective and asymptotic criticality of structurally disordered magnets

Changes in magnetic critical behaviour of quenched structurally-disordered magnets are usually exemplified in experiments and in MC simulations by diluted systems consisting of magnetic and non-magnetic components. In our study we aim to show that similar effects can be observed not only for diluted magnets with non-magnetic impurities but may be implemented, e.g., by the presence of two (and more) chemically different magnetic components as well. Therefore we consider a model of the structurally-disordered quenched magnet where all lattice sites are occupied by Ising-like spins of different lengths L. In such a random spin length Ising model, the length L of each spin is a random variable governed by the distribution function p(L). We demonstrate that this model belongs to the universality class of the site-diluted Ising model. This proves that both models are described by the same values of asymptotic critical exponents. However, their effective critical behaviour differs. As a case study, we consider a quenched mixture of two different magnets with values of elementary magnetic moments L1=1 and L2=s, and of concentration c and 1−c, correspondingly. We apply field-theoretical renormalization group approach to analyse the renormalization group flow for different initial conditions, triggered by s and c, and to calculate effective critical exponents further away from the fixed points of the renormalization group transformation. We show how the effective exponents are governed by difference in properties of the magnetic components.

Phases of the spin- 12 Heisenberg antiferromagnet on the diamond-decorated square lattice in a magnetic field

The spin-1/2 Heisenberg antiferromagnet on the frustrated diamond-decorated square lattice is known to feature various zero-field ground-state phases, consisting of extended monomer-dimer and dimer-tetramer ground states as well as a ferrimagnetic regime. Using a combination of analytical arguments, density matrix renormalization group (DMRG), exact diagonalization as well as sign-problem-free quantum Monte Carlo (QMC) calculations, we investigate the properties of this system and the related Lieb lattice in the presence of a finite magnetic field, addressing both the ground-state phase diagram as well as several thermodynamic properties. In addition to the zero-field ground states, we find at high magnetic field a spin-canted phase with a continuously rising magnetization for increasing magnetic field strength as well as the fully polarized paramagnetic phase. At intermediate field strength, we identify a first-order quantum phase transition line between the ferrimagnetic and the monomer-dimer regime. This first-order line extends to finite temperatures, terminating in a line of critical points that belong to the universality class of the two-dimensional Ising model.

Antiferromagnetic Ising model with frustration on Graphenylene lattice

Frustration effects due to competition between nearest-neighbor and next-nearest-neighbor spins interaction on the graphenylene lattice, also known as biphenylene carbon lattice, were investigated by Monte Carlo simulations. We identified two possible phases from our results of the entropy at zero temperature, namely an ordered spin glass and other an antiferromagnetic phase. Despite the complexity of the lattice, a finite size scaling analysis for the antiferromagnetic regime shows that it can be classified into the same universality class of the usual Ising model. The canonical probability distribution as a function of the spin glass order parameter was computed and the continuous spin glass phase transition confirmed.

Anomalous spin dynamics in a two-dimensional magnet induced by anisotropic critical fluctuations

We investigate the temperature dependence of $g$ factor in two-dimensional (2D) ferromagnet ${\mathrm{CrSiTe}}_{3}$ by combining three-dimensional vector-ferromagnetic resonance (FMR) experiments. It is shown from the angular dependence that the dramatic $g$ shift near critical temperature originates from the interplay of enhanced magnetic fluctuations and anisotropic spin interactions in 2D magnetism. The crossover from isotropic to anisotropic $g$ factor for $T\ensuremath{\rightarrow}{T}_{c}$ yields anomalously parallel pumped excitations. In the critical regime, the field suppression of critical fluctuations is associated with the field dependence of $g$ shift. Furthermore, the results of FMR $g$ shift are scaled by susceptibilities and spontaneous magnetization obtained from magnetometry measurements, which show good agreement with the universality class of the 2D Ising model.

Phase transition of four-dimensional lattice ϕ4 theory with tensor renormalization group

We investigate the phase transition of the four-dimensional single-component ${\ensuremath{\phi}}^{4}$ theory on the lattice using the tensor renormalization group method. We have examined the hopping parameter dependence of the bond energy and the vacuum condensation of the scalar field $⟨\ensuremath{\phi}⟩$ at a finite quartic coupling $\ensuremath{\lambda}$ on large volumes up to $V=102{4}^{4}$ in order to detect the spontaneous breaking of the ${\mathbb{Z}}_{2}$ symmetry. Our results show that the system undergoes the weak first-order phase transition at a certain critical value of the hopping parameter. We also make a comparative study of the three-dimensional ${\ensuremath{\phi}}^{4}$ theory and find that the properties of the phase transition are consistent with the universality class of the three-dimensional Ising model.

Exact fluctuating hydrodynamics of active lattice gases—typical fluctuations

We extend recent results on the exact hydrodynamics of a system of diffusive active particles displaying a motility-induced phase separation to account for typical fluctuations of the dynamical fields. By calculating correlation functions exactly in the homogeneous phase, we find that two macroscopic length scales develop in the system. The first is related to the diffusive length of the particles and the other to the collective behavior of the particles. The latter diverges as the critical point is approached. Our results show that the critical behavior of the model in one dimension belongs to the universality class of a mean-field Ising model, both for static and dynamic properties, when the thermodynamic limit is taken in a specified manner. The results are compared to the critical behavior exhibited by the ABC model. In particular, we find that in contrast to the ABC model the density large deviation function, at its Gaussian approximation, does not contain algebraically decaying interactions but is of a finite, macroscopic, extent which is dictated by the diverging correlation length.

Dynamic phase transition properties and metamagnetic anomalies of kinetic Ising model in the presence of additive white noise

Using Monte Carlo simulations based on the Metropolis algorithm, we investigate the dynamic phase transition properties of a kinetic Ising model driven by a sinusoidally oscillating magnetic field in the presence of additive white noise, as well as a time independent bias term. By performing a detailed finite-size scaling analysis, we estimate the critical exponent ratios corresponding to the dynamic order parameter and the associated scaled variance, and we calculate the critical field below which the system exhibits a dynamic ferromagnetic phase. As a general result, we show that for a noisy system, DPT does not fall into the conventional universality class of the two-dimensional kinetic Ising model. Finally, as a peculiar phenomenon observed in dynamic phase transitions, we explore the evolution of anomalous metamagnetic fluctuations as a function of the noise. Our results show evidence that the bias field at which the metamagnetic anomaly occurs tends to extend towards the oscillation amplitude of the periodic magnetic field.

Strangeness-neutral equation of state for QCD with a critical point

We present a strangeness-neutral equation of state for QCD that exhibits critical behavior and matches lattice QCD results for the Taylor-expanded thermodynamic variables up to fourth order in $$\mu _B/T$$ . It is compatible with the SMASH hadronic transport approach and has a range of temperatures and baryonic chemical potentials relevant for phase II of the Beam Energy Scan at RHIC. We provide an updated version of the software BES-EoS, which produces an equation of state for QCD that includes a critical point in the 3D Ising model universality class. This new version also includes isentropic trajectories and the critical contribution to the correlation length. Since heavy-ion collisions have zero global net-strangeness density and a fixed ratio of electric charge to baryon number, the BES-EoS is more suitable to describe this system. Comparison with the previous version of the EoS is thoroughly discussed.

Order by disorder in frustration-free systems: Quantum Monte Carlo study of a two-dimensional PXP model

In this study, an order by disorder mechanism has been proposed in a two-dimensional PXP model, where the extensive degeneracy of the classical ground-state manifold is due to strict occupation constraints instead of geometrical frustrations. By performing an unbias large-scale quantum monte carlos simulation, we find that local quantum fluctuations, which usually work against long-range ordering, lift the macroscopic classical degeneracy and give rise to a compressible ground state with charge-density-wave long-range order. A simple trial wavefunction has been proposed to capture the essence of the ground-state of the two-dimensional PXP model. The finite temperature properties of this model have also been studied, and we find a thermal phase transition with an universality class of two-dimensional Ising model.

Mixed-order transition in the antiferromagnetic quantum Ising chain in a field

The antiferromagnetic quantum Ising chain has a quantum critical point which belongs to the universality class of the transverse Ising model (TIM). When a longitudinal field ($h$) is switched on, the phase transition is preserved, which turns to first-order for $h/\Gamma \to \infty$, $\Gamma$ being the strength of the transverse field. Here we will re-examine the critical properties along the phase transition line. During a quantum block renormalization group calculation, the TIM fixed point for $h/\Gamma>0$ is found to be unstable. Using DMRG techniques, we calculated the entanglement entropy and the spin-spin correlation function, both of which signaled a divergent correlation length at the transition point with the TIM exponents. At the same time, the bulk correlation function has a jump and the end-to-end correlation function has a discontinuous derivative at the transition point. Consequently for finite $h/\Gamma$ the transition is of mixed-order.

Short-time Monte Carlo simulation of the majority-vote model on cubic lattices

We perform short-time Monte Carlo simulations to study the criticality of the isotropic two-state majority-vote model on cubic lattices of volume N=L3, with L up to 2048. We obtain the precise location of the critical point by examining the scaling properties of a new auxiliary function Ψ. We perform finite-time scaling analysis to accurately calculate the whole set of critical exponents, including the dynamical critical exponent z=2.027(9), and the initial slip exponent θ=0.1081(1). Our results indicate that the majority-vote model in three dimensions belongs to the same universality class of the three-dimensional Ising model.

Tensor network study of the m=12 magnetization plateau in the Shastry-Sutherland model at finite temperature

The two-dimensional infinite projected entangled pair states tensor network is evolved in imaginary time with the full update (FU) algorithm to simulate the Shastry-Sutherland model in a magnetic field at finite temperature directly in the thermodynamic limit. We focus on the phase transition into the $m=1/2$ magnetization plateau, which was observed in experiments on SrCu$_2$(BO$_3$)$_2$. For the largest simulated bond dimension, the early evolution in the high-temperature regime is simulated with the simple update (SU) scheme and then, as the correlation length increases, continued with the FU scheme towards the critical regime. We apply a small symmetry-breaking bias field and then extrapolate towards zero bias using a simple scaling theory in the bias field. The combined SU + FU scheme provides an accurate estimate of the critical temperature, even though the results could not be fully converged in the bond dimension in the vicinity of the transition. The critical temperature estimate is improved with a generalized scaling theory that combines two divergent length scales: One due to the bias, and the other due to the finite bond dimension. The obtained results are consistent with the transition being in the universality class of the two-dimensional classical Ising model. The estimated critical temperature is $3.5(2)$ K, which is well above the temperature $2.1$ K used in the experiments.

Effect of Confinement on Capillary Phase Transition in Granular Aggregates.

Using a 3D mean-field lattice-gas model, we analyze the effect of confinement on the nature of capillary phase transition in granular aggregates with varying disorder and their inverse porous structures obtained by interchanging particles and pores. Surprisingly, the confinement effects are found to be much less pronounced in granular aggregates as opposed to porous structures. We show that this discrepancy can be understood in terms of the surface-surface correlation length with a connected path through the fluid domain, suggesting that this length captures the true degree of confinement. We also find that the liquid-gas phase transition in these porous materials is of second order nature near capillary critical temperature, which is shown to represent a true critical temperature, i.e., independent of the degree of disorder and the nature of the solid matrix, discrete or continuous. The critical exponents estimated here from finite-size scaling analysis suggest that this transition belongs to the 3D random field Ising model universality class as hypothesized by F. Brochard and P.G. de Gennes, with the underlying random fields induced by local disorder in fluid-solid interactions.

Superradiance, bosonic Peierls distortion, and lattice gauge theory in a generalized Rabi-Hubbard chain

We investigate a one-dimensional Rabi-Hubbard type of model, arranged such that a qdot is sandwiched between every cavity. The role of the qdot is to transmit photons between neighboring cavities, while simultaneously acting as a photon non-linearity. We consider three-level qdots in the $\Lambda$ configuration, where the left and right leg couples exclusively to the left or right cavity. This non-commuting interaction leads to two highly entangled incompressible phases, separated by a second order quantum phase transition: the qdot degrees-of-freedom act as a dynamical lattice for the photons and a Peierls instability breaks a second $\mathbb{Z}_2$ symmetry which leads to a dimerization in entanglement and photon number. We also find a normal insulating phase and a superfluid phase that acts as a quantum many-body superradiant phase. In the superradiant phase, a $\mathbb{Z}_2$ symmetry is broken and the phase transition falls within the transverse field Ising model universality class. Finally, we show that a limit of the model can be interpreted as a $\mathbb{Z}_2$ lattice gauge theory.

Gaussian trajectory approach to dissipative phase transitions: The case of quadratically driven photonic lattices

We apply the Gaussian trajectories approach to the study of the critical behavior of two-dimensional dissipative arrays of nonlinear photonic cavities, in presence of two-photon driving and in regimes of sizable loss rates. In spite of the highly mixed character of the density matrix of this system, the numerical approach is able to provide precise estimations of the steady-state expectation values, even for large lattices made of more than 100 sites. By performing a finite-size scaling of the relevant properties of the steady state, we extrapolate the behavior of the system in the thermodynamic limit and we show the emergence of a second-order dissipative phase transition, belonging to the universality class of thermal Ising model. This result indicates the occurrence of a crossover when the loss rate is increased from the weak-loss limit, in which the phase transition belongs to the universality class of the quantum Ising model

Classical critical dynamics in quadratically driven Kerr resonators

Driven-dissipative kerr lattices with two-photon driving are experimentally relevant systems known to exhibit a symmetry-breaking phase transition, which belongs to the universality class of the thermal Ising model for the parameter regime studied here. In this work, we perform finite-size scaling of this system as it is quenched to the transition and the dynamical critical exponent is found to be compatible with $z\approx2.18$ corresponding with metropolis dynamics in classical simulations. Furthermore, we show that the Liouvillian gap scales with the same exponent, similar to scaling of the Hamiltonian gap at quantum phase transitions in closed systems.