An Improved Heterogeneous Mean-Field Theory for the Ising Model on Complex Networks

Heterogeneous mean-field theory is commonly used methodology to study dynamical processes on complex networks,such as epidemic spreading and phase transitions in spin models.In this paper,we propose an improved heterogeneous mean-field theory for studying the Ising model on complex networks.Our method shows a more accurate prediction in the critical temperature of the Ising model than the previous heterogeneous mean-field theory.The theoretical results are validated by extensive Monte Carlo simulations in various types of networks.     

Novel domain growth law in random magnets

We investigate the kinetics of domain growth in Ising magnets where a fraction 1 - p of the magnetic atoms or ions (spins) are randomly substituted by non-magnetic impurities. We argue that close to the percolation threshold p_c, the statistical self-similarity of the underlying structure gives rise to a novel crossover in the growth law. We propose a method to detect any evidence of this new prediction from the kinetics of domain growth in the dilute Ising model (DIM) during intermediate time scales by carrying out Monte Carlo simulations not at p = p_c but at slightly higher spin concentrations. We analyze the results of our extensive Monte Carlo simulation of the strongly diluted two-dimensional Ising model and find the growth to be consistent with the proposed scenario. We also compare our observations with those in the recent experiments on the kinetics of ordering in Rb₂Co_pMg_1−pF₄.     

Nonequilibrium wetting transition in a nonthermal 2D Ising model

Nonequilibrium wetting transitions are observed in Monte Carlo simulations of a kinetic spin system in the absence of a detailed balance condition with respect to an energy functional. A nonthermal model is proposed starting from a two-dimensional Ising spin lattice at zero temperature with two boundaries subject to opposing surface fields. Local spin excitations are only allowed by absorbing an energy quantum (photon) below a cutoff energy E _c . Local spin relaxation takes place by emitting a photon which leaves the lattice. Using Monte Carlo simulation nonequilibrium critical wetting transitions are observed as well as nonequilibrium first-order wetting phenomena, respectively in the absence or presence of absorbing states of the spin system. The transitions are identified from the behavior of the probability distribution of a suitably chosen order parameter that was proven useful for studying wetting in the (thermal) Ising model.     

A new Monte Carlo power method for the eigenvalue problem of transfer matrices

We propose a new Monte Carlo method for calculating eigenvalues of transfer matrices leading to free energies and to correlation lengths of classical and quantum many-body systems. Generally, this method can be applied to the calculation of the maximum eigenvalue of a nonnegative matrix  such that all the matrix elements of Â^k are strictly positive for an integerk. This method is based on a new representation of the maximum eigenvalue of the matrix  as the thermal average of a certain observable of a many-body system. Therefore one can easily calculate the maximum eigenvalue of a transfer matrix leading to the free energy in the standard Monte Carlo simulations, such as the Metropolis algorithm. As test cases, we calculate the free energies of the square-lattice Ising model and of the spin-1/2XY Heisenberg chain. We also prove two useful theorems on the ergodicity in quantum Monte Carlo algorithms, or more generally, on the ergodicity of Monte Carlo algorithms using our new representation of the maximum eigenvalue of the matrixÂ.     

Absence of an Almeida-Thouless line in three-dimensional spin glasses

We present results of Monte Carlo simulations of the three-dimensional Edwards-Anderson Ising spin glass in the presence of a (random) field. A finite-size scaling analysis of the correlation length shows no indication of a transition, in contrast with the zero-field case. This suggests that there is no Almeida-Thouless line for short-range Ising spin glasses.     

Universality aspects of the 2d random-bond Ising and 3d Blume-Capel models

We report on large-scale Wang-Landau Monte Carlo simulations of the critical behavior of two spin models in two- (2d) and three-dimensions (3d), namely the 2d random-bond Ising model and the pure 3d Blume-Capel model at zero crystal-field coupling. The numerical data we obtain and the relevant finite-size scaling analysis provide clear answers regarding the universality aspects of both models. In particular, for the random-bond case of the 2d Ising model the theoretically predicted strong universality’s hypothesis is verified, whereas for the second-order regime of the Blume-Capel model, the expected d = 3 Ising universality is verified. Our study is facilitated by the combined use of the Wang-Landau algorithm and the critical energy subspace scheme, indicating that the proposed scheme is able to provide accurate results on the critical behavior of complex spin systems.     

Low-temperature broken-symmetry phases of spiral antiferromagnets

We study Heisenberg antiferromagnets with nearest- (J1) and third- (J3) neighbor exchange on the square lattice. In the limit of spin S-->infinity, there is a zero temperature (T) Lifshitz point at J(3)=1/4J(1), with long-range spiral spin order at T=0 for J3>1/4J(1). We present classical Monte Carlo simulations and a theory for T>0 crossovers near the Lifshitz point: spin rotation symmetry is restored at any T>0, but there is a broken lattice reflection symmetry for 0< or =T相似文献   

Behavior of Ising spin glasses in a magnetic field

We study the existence of a spin-glass phase in a field using Monte Carlo simulations performed along a nontrivial path in the field-temperature plane that must cross any putative de Almeida-Thouless instability line. The method is first tested on the Ising spin glass on a Bethe lattice where the instability line separating the spin glass from the paramagnetic state is also computed analytically. While the instability line is reproduced by our simulations on the mean-field Bethe lattice, no such instability line can be found numerically for the short-range three-dimensional model.     

Phase transitions and universality in nonequilibrium steady states of stochastic Ising models

We present results of direct computer simulations and of Monte Carlo renormalization group (MCRG) studies of the nonequilibrium steady states of a spin system with competing dynamics and of the voter model. The MCRG method, previously used only for equilibrium systems, appears to give useful information also for these nonequilibrium systems. The critical exponents are found to be of Ising type for the competing dynamics model at its second-order phase transitions, and of mean-field type for the voter model (consistent with known results for the latter).     

Nonequilibrium dynamics in two-dimensional Ising spin glass

This paper investigates the nonequilibrium dynamics of two-dimensional Ising spin glass by dynamical Monte Carlo simulations. A new method is developed to quantitatively measure the age of domain growth. Using this method it investigates how temperature shift affects the effective age of domain growth. It finds that the T -shift dependence of the effective age follows the prediction of the droplet model quite well. It also investigates the overlap length between the spin glass states as well as the correlated flips of spins,which are not consistent with the theoretical predictions. The possible reasons are discussed.     

Monte Carlo study of an Ising gauge system

The phase diagram of the 3-d Ising gauge model with additional ferromagnetic nearest neighbour Ising coupling is explored by Monte Carlo simulations.     

Ising transition driven by frustration in a 2D classical model with continuous symmetry

We study the thermal properties of the classical antiferromagnetic Heisenberg model with both nearest (J1) and next-nearest (J2) exchange couplings on the square lattice by extensive Monte Carlo simulations. We show that, for J2/J1>1/2, thermal fluctuations give rise to an effective Z2 symmetry leading to a finite-temperature phase transition. We provide strong numerical evidence that this transition is in the 2D Ising universality class, and that T(c)-->0 with an infinite slope when J2/J1-->1/2.     

Multi-step magnetization of the Ising model on a Shastry-Sutherland lattice: a Monte?Carlo simulation

The magnetization behaviors and spin configurations of the classical Ising model on a Shastry-Sutherland lattice are investigated using Monte Carlo simulations, in order to understand the fascinating magnetization plateaus observed in TmB(4) and other rare-earth tetraborides. The simulations reproduce the 1/2 magnetization plateau by taking into account the dipole-dipole interaction. In addition, a narrow 2/3 magnetization step at low temperature is predicted in our simulation. The multi-step magnetization can be understood as the consequence of the competitions among the spin-exchange interaction, the dipole-dipole interaction, and the static magnetic energy.     

On the universality class of the 3d Ising model with long-range-correlated disorder

We analyze a controversial topic about the universality class of the three-dimensional Ising model with long-range-correlated disorder. Whereas both theoretical and numerical studies agree on the validity of the extended Harris criterion [A. Weinrib, B.I. Halperin, Phys. Rev. B 27 (1983) 413] and indicate the existence of a new universality class, numerical values of the critical exponents found so far differ considerably. To resolve this discrepancy we perform extensive Monte Carlo simulations of a 3d Ising model with non-magnetic impurities being arranged in a form of lines along randomly chosen axes of a lattice. The Swendsen-Wang algorithm is used alongside with a histogram reweighting technique and finite-size scaling analysis to evaluate the values of critical exponents governing magnetic phase transition. Our estimates for these exponents differ from both previous numerical simulations and are in favor of a non-trivial dependency of the critical exponents on the peculiarities of long-range correlation decay.     

Ising droplets in five dimensions

Monte Carlo simulations indicate that the size distribution of Coniglio-Klien droplets in the five-dimensional nearest-neighbor Ising model corresponds to mean field Ising exponents.     

Replica symmetry breaking transition of the weakly anisotropic Heisenberg spin glass in magnetic fields

The spin and the chirality orderings of the three-dimensional Heisenberg spin glass with the weak random anisotropy are studied under applied magnetic fields by equilibrium Monte Carlo simulations. A replica symmetry breaking transition occurs in the chiral sector accompanied by the simultaneous spin-glass order. The ordering behavior differs significantly from that of the Ising spin glass, despite the similarity in the global symmetry. Our observation is consistent with the spin-chirality decoupling-recoupling scenario of a spin-glass transition.     

Self-diffusion and ‘order–order’ kinetics in B2-ordering AB binary systems with a tendency for triple-defect formation: Monte Carlo simulation

Self-diffusion of component atoms and ‘order–order’ relaxations in a B2-ordering binary system AB showing a tendency for triple-defect formation were consistently simulated by means of two Monte Carlo techniques. In view of a strict correlation between antisite-defect and vacancy concentrations the Kinetic Monte Carlo (KMC) simulations were implemented with a temperature-dependent vacancy concentration determined by means of Semi-Grand Canonical Monte Carlo (SGCMC) simulations. The Ising model of the system was completed with local-configuration-dependent saddle-point energy parameters related to vacancy mediated atomic jumps. The simulations elucidated the atomistic origin of the experimentally observed low rate of ‘order–order’ relaxations in NiAl, as well as reproduced the experimental relation between the activation energies for ‘order–order’ kinetics and Ni self-diffusion in NiAl. Higher value of the deduced activation energy for atomic migration with respect to the effective energy barriers related to individual atomic jumps indicated their high correlation.     

Mixed Ising ferrimagnets with next-nearest-neighbour couplings on square lattices

We study Ising ferrimagnets on square lattices with antiferromagnetic exchange couplings between spins of values S = 1/2 and 1 on neighbouring sites, couplings between S = 1 spins at next-nearest-neighbour sites of the lattice and a single-site anisotropy term for the S = 1 spins. Using mainly ground state considerations and extensive Monte Carlo simulations, we investigate various aspects of the phase diagram, including compensation points, critical properties and temperature-dependent anomalies. In contrast to previous belief, the next-nearest-neighbour couplings, when being of antiferromagnetic type, may lead to compensation points.     

Simulations on infinite-size lattices

We introduce a Monte Carlo method, as a modification of existing cluster algorithms, which allows simulations directly on systems of infinite size, and for quantum models also at beta = infinity. All two-point functions can be obtained, including dynamical information. When the number of iterations is increased, correlation functions at larger distances become available. Limits q-->0 and omega-->0 can be approached directly. As examples we calculate spectra for the d = 2 Ising model and for Heisenberg quantum spin ladders with two and four legs.     

Dielectric properties and compensation behaviors of a monolayer naphthalene-like nanoisland: Monte Carlo simulations

In this paper, we propose a model to study the thermal and dielectric properties of a monolayer naphthalene-like nanoisland. The ferrielectric mixed spin (1, 7/2) Blume-Capel Ising model has been studied, using Monte Carlo simulations under the Metropolis algorithm. The ground state phase diagrams, in the absence of temperature, are investigated. Moreover, we illustrated the thermal and dielectric properties as a function of temperature, for fixed values of the other parameters. On the other hand, we examine the effects of the exchange coupling interactions on the compensation and blocking temperatures. In addition, we explore the effects of crystal and external longitudinal electric fields on total polarizations.