二维无规混合磁性系统磁特性的微磁学及Monte Carlo研究

采用能量极小原理的微磁学及Monte Carlo方法对异类自旋组成混合Heisenberg自旋体系进行模拟计算,研究了二维铁磁反铁磁无规混合系统的磁特性.发现了二维无规混合磁性系统存在M-H磁化曲线的阶梯效应.通过一维Ising模型及系统能量、自旋组态的研究,发现小自旋数目的反铁磁耦合系统是产生M-H阶梯效应的根本原因.     

Convergence to Equilibrium of Random Ising Models in the Griffiths Phase

We consider Glauber-type dynamics for disordered Ising spin systems with nearest neighbor pair interactions in the Griffiths phase. We prove that in a nontrivial portion of the Griffiths phase the system has exponentially decaying correlations of distant functions with probability exponentially close to 1. This condition has, in turn, been shown elsewhere to imply that the convergence to equilibrium is faster than any stretched exponential, and that the average over the disorder of the time-autocorrelation function goes to equilibrium faster than exp[–k(log t) ^d/(d–1)]. We then show that for the diluted Ising model these upper bounds are optimal.     

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.     

Monte Carlo simulation of a random-field Ising antiferromagnet

Phase transitions in the three-dimensional diluted Ising antiferromagnet in an applied magnetic field are analyzed numerically. It is found that random magnetic field in a system with spin concentration below a certain threshold induces a crossover from second-order phase transition to first-order transition to a new phase characterized by a spin-glass ground state and metastable energy states at finite temperatures.     

三维Ising模型的蒙特卡罗模拟

采用蒙特卡罗(Monte Carlo)重点抽样法对三维Ising模型进行计算机模拟,测量无外磁场时三维Ising模型中自旋键链的能量、磁化强度、比热及磁化率的统计平均值与标准误差(不确定度).结果表明,三维Ising模型在无外磁场时存在自发磁化现象,铁磁→非铁磁相变临界点在J/(k_BT_C)=0.222 0,或居里温度T_C=4.500 0处.并研究存在外磁场时上述物理量随温度与外磁场的变化规律,给出物理解释.     

Monte Carlo simulation of three-dimensional dilute Ising model

A multispin coding program for site-diluted Ising models on large simple cubic lattices is described in detail. The spontaneous magnetization is computed as a function of temperature, and the critical temperature as a function of concentration is found to agree well with the data of Marro et al.⁽⁴⁾ and Landau⁽³⁾ for smaller systems.The first successful epsilon expansion seems to be by D. E. Khmelnitskii,ZhETF 68:1960 (1975), English translationSov. Phys. JETP 41:981 (1975); for numerical estimates see K. E. Newman and E. K. Riedel,Phys. Rev. H25:264 (1982), for experiments see R. J. Birgenau, R. A. Cowley, G. Shirane and H. Yoshizawa,J. Stat. Phys. 34:817 (1984).     

Single-cluster Monte Carlo dynamics for the Ising model

We present an extensive study of a new Monte Carlo acceleration algorithm introduced by Wolff for the Ising model. It differs from the Swendsen-Wang algorithm by growing and flipping single clusters at a random seed. In general, it is more efficient than Swendsen-Wang dynamics ford>2, giving zero critical slowing down in the upper critical dimension. Monte Carlo simulations give dynamical critical exponentsz _w=0.33±0.05 and 0.44+0.10 ind=2 and 3, respectively, and numbers consistent withz _w=0 ind=4 and mean-field theory. We present scaling arguments which indicate that the Wolff mechanism for decorrelation differs substantially from Swendsen-Wang despite the apparent similarities of the two methods.     

Series and Monte Carlo study of high-dimensional Ising models

Ising models in high dimensions are used to compare high-temperature series expansions with Monte Carlo simulations. Simulations of the magnetization on four-, six-, and seven-dimensional hypercubic lattices give consistent values of the critical temperature from both equilibrium and nonequilibrium data ford=6 and 7. We tabulate 15 terms of series expansions for the susceptibility for generald and giveJ/k _B T _c =0.092295 (3) and 0.077706 (2) ford=6 and 7. In contrast to five dimensions, where earlier series found nonanalytic scaling corrections, for d=6 and 7 the leading scaling correction may be analytic inT-T _c . In most cases these expansions gave more accurate results than these simulations.     

Monte Carlo simulation of cluster kinetics in three-dimensional Ising model

Simulations in lattices of size 100³ at the critical point of the three-dimensional Glauber kinetic Ising model indicate that the 1935 Becker-Doring equation no longer works there: The growth rates decay in time. These conclusions confirm those in two dimensions.     

Monte Carlo simulation of very large kinetic Ising models

We study the relaxation of Ising models in three and four dimensions aboveT _c , using multi-spin coding for lattices up to 360³ and 40⁴. The nonlinear relaxation time diverges as (T–T _c )^{–1.05±0.04} in three dimensions, where corrections to scaling are taken into account. In four dimensions the effective exponent is about 0.72; logarithmic correction factors make the analysis difficult here. The linear relaxation time for the asymptotic exponential decay is found to be larger, with effective exponents 1.31 (d=2) and 0.97 (d=4). The difference in the linear and nonlinear relaxation exponents is compatible in three dimensions with the orderparameter exponent , as predicted by Racz.Work supported by SFB 125 Aachen-Jülich-KölnWork started at Department de Physique des Systemes Desordonnes, Universite de Provence, Centre St-Jerome, F-13397 Marseille Cedex 13, France     

Magnetic Impurity Band and Photoinduced Magnetic Phase Transition in Diluted Magnetic Semiconductors

Applying the dynamical coherent potential approximation (dynamical CPA) to a model of diluted magnetic semiconductors (DMSs), in which both random impurity distribution and thermal fluctuation of localized spins are taken into account, the spin-polarized band and the carrier spin polarization are calculated for various magnetizations. In order to clarify the role of impurity depth on the occurrence of ferromagnetism, three typical cases are investigated: (a) II-VI DMS, (b) deep impurity level, and (c) strong exchange interaction. The present study reveals that the impurity depth of magnetic ions strongly enhances the carrier spin polarization (CSP) and accordingly, leads to a high Curie temperature. This means that photoinduced ferromagnetism with high Curie temperature can be expected in a DMS with a deep impurity depth and strong exchange interaction.     

A Monte Carlo Sampling Scheme for the Ising Model

In this paper we describe a Monte Carlo sampling scheme for the Ising model and similar discrete-state models. The scheme does not involve any particular method of state generation but rather focuses on a new way of measuring and using the Monte Carlo data. We show how to reconstruct the entropy S of the model, from which, e.g., the free energy can be obtained. Furthermore we discuss how this scheme allows us to more or less completely remove the effects of critical fluctuations near the critical temperature and likewise how it reduces critical slowing down. This makes it possible to use simple state generation methods like the Metropolis algorithm also for large lattices.     

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.     

Tests for Monte Carlo renormalization studies on Ising models

In this expanded version of an earlier letter, we consider many computational details that were omitted for want of space. Ford = 2 Ising spins with up to 13 different short-range interactions, we construct the critical surface in the vicinity of (Onsager's) nearest-neighbor (nn) critical point by using the body of the available information on the solvable nn case. We then see if the Monte Carlo renormalization group flows generated from this point do indeed lie on this surface and quantify the errors if they do not.     

Monte Carlo study of surface roughening in the three-dimensional Ising model

Above a roughening temperature of about 0.56T _c the thickness of the two-dimensional interface separating domain on a simple cubic lattice is found to increase roughly logarithmically with system size. Also, the interface tension is determined for temperatures belowT _c.     

Monte Carlo study of the Yukawa coupled two-spin Ising model

We consider a particular four state spin system composed of two Ising spins (s_x, σ_x) with independent hopping parameters κ₁ κ₂, coupled by a bilinear Yukawa term, ys_xσ_x. The Yukawa term is solely responsible for breaking the global Z₂ × Z₂ symmetry down to Z2. This model is intended as an illustration of general coupled Higgs system where scalars can arise both as composite and elementary excitations. For the Ising example in 2d, we give convincing numerical evidence of the universality of the two-spin system with the one-spin Ising model, by Monte Carlo simulations and finite size scaling analysis. We also show that as we approach the phase transition, universality arises by having a single correlation length that diverges.     

Monte Carlo calculation of phase separation in a two-dimensional Ising system

Journal of Statistical Physics - Monte Carlo calculations were carried out for a two-dimensional Ising model of a binary alloy with nearest-neighbor attractive interactions between like atoms. The...     

Relaxation to Equilibrium for Two Dimensional Disordered Ising Systems in the Griffiths Phase

We consider Glauber–type dynamics for two dimensional disordered magnets of Ising type. We prove that, if the disorder–averaged influence of the boundary condition is sufficiently small in the equilibrium system, then the corresponding Glauber dynamics is ergodic with probability one and the disorder–average C(t) of time–autocorrelation function satisfies (for large t). For the standard two dimensional dilute Ising ferromagnet with i.i.d. random nearest neighbor couplings taking the values 0 or J ₀>0, our results apply even if the active bonds percolate and J ₀ is larger than the critical value J _c of the corresponding pure Ising model. For the same model we also prove that in the whole Griffiths' phase the previous upper bound is optimal. This implies the existence of a dynamical phase transition which occurs when J crosses J _c . Received: