A Markov-property Monte Carlo method: One-dimensional Ising model

In this paper we introduce a new Monte Carlo procedure based on the Markov property. This procedure is particularly well suited to massively parallel computation. We illustrate the method on the critical phenomena of the well known one-dimensional Ising model. In the course of this work we found that the autocorrelation time for the Metropolis Monte Carlo algorithm is closely given by the square of the correlation length. We find speedup factors of the order of 1 million for the method as implemented on the CM2 relative to a serial machine. Our procedure gives error estimates which are quite consistent with the observed deviations from the analytically known exact results.     

Critical dynamics of the three-dimensional Ising model: A Monte Carlo study

Extensive Monte Carlo simulations have been performed to analyze the dynamical behavior of the three-dimensional Ising model with local dynamics. We have studied the equilibrium correlation functions and the power spectral densities of odd and even observables. The exponential relaxation times have been calculated in the asymptotic one-exponential time region. We find that the critical exponentz=2.09 ±0.02 characterizes the algebraic divergence with lattice size for all observables. The influence of scaling corrections has been analyzed. We have determined integrated relaxation times as well. Their dynamical exponentz _int agrees withz for correlations of the magnetization and its absolute value, but it is different for energy correlations. We have applied a scaling method to analyze the behavior of the correlation functions. This method verifies excellent scaling behavior and yields a dynamical exponentz _scal which perfectly agrees withz.     

Ising模型的并行计算

以Ising模型为例,介绍有关格点系统的Monte Carlo数值模拟并行算法的设计和编程,并给出在本组建造的PC集群式高性能并行计算系统上的测量结果.本文的结果对格点量子色动力学的大规模数值模拟研究有一定的参考价值     

Monte Carlo technique for very large ising models

Rebbi's multispin coding technique is improved and applied to the kinetic Ising model with size 600*600*600. We give the central part of our computer program (for a CDC Cyber 76), which will be helpful also in a simulation of smaller systems, and describe the other tricks necessary to go to large lattices. The magnetizationM atT=1.4*T _c is found to decay asymptotically as exp(-t/2.90) ift is measured in Monte Carlo steps per spin, and M(t = 0) = 1 initially.     

Monte Carlo simulation of the compensation and critical behaviors of a ferrimagnetic core/shell nanoparticle Ising model

A Monte Carlo simulation has been used to study the magnetic properties and the critical behaviors of a single spherical nanoparticle, consisting of a ferromagnetic core of spins surrounded by a ferromagnetic shell of S=±1, 0 or , spins with antiferromagnetic interface coupling, located on a simple cubic lattice. A number of characteristic phenomena has been found. In particular, the effects of the shell coupling and the interface coupling on both the critical and compensation temperatures are investigated. We have found that, for appropriate values of the system parameters, two compensation temperatures may occur in the present system.     

A new multispin coding algorithm for Monte Carlo simulation of the Ising model

We present a new algorithm for Monte Carlo simulation of the Ising model. The usual serial architecture of a computer is exploited in a novel way, enabling parallel but independent calculations to be carried out on as many spins as there are bits in a computer word in each fundamental move. The algorithm enjoys a substantial increase in execution speed over more usual multispin coding algorithms. By its very nature, the algorithm constitutes a design for a special-purpose processor.     

Monte Carlo study of the critical behavior of pure and site-diluted Ising ferro-and ferrimagnets

Monte Carlo simulations are performed for pure and site-diluted Ising ferro- and ferrimagnets on a simple cubic lattice with up to 40³ sites and with impurity concentrationx. For the diluted ferromagnet (x=0.2) the exponent= 0.392±0.03 is definitely larger than the pure model value of=0.304±0.03. In contrast, for ferrimagnetic systems (x=0, 0.1, 0.2) the values appear to be independent ofx and within the error limits consistent with the value for the pure ferromagnet, possibly because the width of the asymptotic random critical regime (or of the crossover regime) is even smaller than in the case of ferromagnets.     

Do the simple and 2/3 majority models belong to the same universality class?: A monte carlo approach

We extend the majority model (introduced by Tsallis in 1982) in the sense that the required majority might be different from the simple majority. We simulate these models for typical cases which include simple and 2/3 majorities. We exhibit the average cluster size as well as the order parameter as functions ofp, the concentration of one of the two possible constituents. No crossover exists between the simple- and non-simple-majority models.     

The Markov property method applied to Ising model calculations

An efficient method of computation for models possessing the Markov property is set out. We apply this method to the two-dimensional ising model and report exact computations for up to 10 by 10 models with periodic boundary conditions. We find that critical-point, finite-size rounding is quite large in the renormalized coupling constant, which is not divergent at the critical point, in contrast to the energy, which is also not divergent and has no rounding there. The difference is traced to the continuity of the energy and the discontinuity of the renormalized coupling constant at the critical point.     

Monte Carlo evidence for a cusp in the uniform susceptibility of the site-diluted simple cubic Ising antiferromagnet

Monte Carlo simulations are performed for pure and site-diluted Ising antiferromagnets on a simple cubic lattice with up to 40³ sites and impurity concentrationx=0, 0.2. and 0.5. Forx=0.5 a cusp emerges for the temperature dependence of the uniform susceptibility at the critical temperature which is contrasted with the smooth behavior for a pure antiferromagnet, in agreement with the theoretical prediction of Fishman and Aharony.     

Dynamical analysis of low-temperature monte carlo cluster algorithms

We present results on the Swendsen-Wang dynamics for the Ising ferromagnet in the low-temperature case without external field in the thermodynamic limit. We discuss in particular the rate of convergence to the equilibrium Gibbs state in finite and infinite volume, the absence of ergodicity in the infinite volume, and the long-time behavior of the probability distribution of the dynamics for various starting configurations. Our results are purely dynamical in nature in the sense that we never use the reversibility of the process with respect to the Gibbs state, and they apply to a stochastic particle system withnon- Gibbsian invariant measure.     

Monte Carlo simulations of conformal theory predictions for the three-state Potts model

The critical properties of the three-state Potts model are investigated using Monte Carlo simulations. Special interest is given to the measurement of three-point correlation functions and associated universal objects, i.e., structure constants. The results agree well with predictions coming from conformal field theory, confirming, for this example, the correctness of the Coulomb gas formalism and the bootstrap method.     

Universality and Conformal Invariance for the Ising Model in Domains with Boundary

The partition function with boundary conditions for various two-dimensional Ising models is examined and previously unobserved properties of nonformal invariance and universality are established numerically.     

Monte Carlo simulations including energy from an entropic force

Several experimental techniques have shown that the primary response of many materials comes from a heterogeneous distribution of independently relaxing nanoscale regions; but most Monte Carlo simulations have homogeneous correlations. Resolving this discrepancy may require including the energy needed to change the configurational entropy, which is often used in theoretical treatments of thermal fluctuations, but not in computer simulations. Here the local configurational entropy is shown to give a nonlinear correction to the Metropolis algorithm that restores conservation of energy, maintains maximum entropy, and yields heterogeneous correlations. The nonlinear correction also improves agreement between Monte Carlo simulations of the Ising model and measurements of specific heat and structural correlations from the Jahn–Teller distortion in LaMnO₃.     

Monte Carlo study of the magnetic properties of Fe0.9−qMn0.1Alq-disordered alloys

Within the framework of a random site-diluted Ising model with nearest-neighbor interactions, and using the Metropolis algorithm for equilibration and energy minimization, we have computed the ensemble and configurational averages for magnetization per site, magnetic susceptibility and specific heat of Fe_0.9−qMn_0.1Al_q-disordered alloys with 0.1q0.55. In the model, atoms have been randomly distributed on a body-centered cubic lattice in order to simulate the disorder and structure as that obtained in arc-melted Fe_0.9−qMn_0.1Al_q alloys treated at high temperatures during long periods of time and followed by fast quenching. Competitive interactions coming from Fe–Fe ferromagnetic bonds and Fe–Mn and Mn–Mn antiferromagnetic couplings, as well as the Al dilutor effect, have been taken into account in our study. Results allow us to conclude that, in agreement with previous Mössbauer data of the average hyperfine field, for which a comparison is also carried out, the Fe_0.9−qMn_0.1Al_q-disordered alloys are well characterized by a critical concentration at room temperature at around 40 at% Al, for which the system undergoes a transition from a ferromagnetic state to a paramagnetic one. The finite size scaling analysis to obtain the critical Al concentration in the thermodynamic limit, as well as the critical exponents, is also presented and discussed.     

Size dependent thermal hysteresis in spin crossover nanoparticles reflected within a Monte Carlo based Ising-like model

Spin crossover compounds are photo-magnetic bistable molecular magnets with two states in thermodynamic competition: the diamagnetic low-spin state and paramagnetic high-spin state. The thermal transition between the two states is often accompanied by a wide hysteresis, premise for possible application of these materials as recording media. In this paper we study the influence of the system's size on the thermal hysteresis loops using Monte Carlo simulations based on an Arrhenius dynamics applied for an Ising like model with long- and short-range interactions. We show that using appropriate boundary conditions it is possible to reproduce both the drop of hysteresis width with decreasing particle size, the hysteresis shift towards lower temperatures and the incomplete transition, as in the available experimental data. The case of larger systems composed by several sublattices is equally treated reproducing the shrinkage of the hysteresis loop's width experimentally observed.     

Hysteretic behavior of Fe0.9−qMn0.1Alq-disordered alloys: a Monte Carlo study

In this work we have simulated the Fe_0.9−qMn_0.1Al_q alloy series with Al contents ranging from 10 up to 50 at%, and for several system sizes. In the simulation, the atoms are randomly distributed on a body-centered cubic according to the atomic disorder achieved through quenching techniques for the experimental samples. In computing the thermodynamic quantities such as the magnetization per site as a function of an external applied magnetic field, we have employed a Monte Carlo algorithm based on a Metropolis dynamics implemented with a random site-diluted Ising model. In this model, we have taken into account nearest-neighbor interactions for which both the ferromagnetic (Fe–Fe) and antiferromagnetic (Fe–Mn, Mn–Mn) interactions are present. From the simulation of the hysteresis loops at room temperature, the remanence and the coercive force as a function of the Al concentration have been obtained. Finally, a comparison with the previous experimental data on coercivity obtained by means of vibrating sample magnetometry is also carried out and discussed.     

On the critical behavior of the Ising model with mixed two- and three-spin interactions

A study is made of a two-dimensional Ising model with staggered three-spin interactions in one direction and two-spin interactions in the other. The phase diagram of the model and its critical behavior are explored by conventional finite-size scaling and by exploiting relations between mass gap amplitudes and critical exponents predicted by conformal invariance. The model is found to exhibit a line of continuously varying critical exponents, which bifurcates into two Ising critical lines. This similarity of the model with the Ashkin-Teller model leads to a conjecture for the exact critical indices along the nonuniversal critical curve. Earlier contradictions about the universality class of the uniform (isotropic) case of the model are clarified.