Monte Carlo Studies of Random Spin Systems with Complex Structures

复杂结构随机自旋系统的蒙特卡罗研究

基本信息

批准号：
09640469
负责人：
OKABE Yutaka
金额：
$ 1.54万
依托单位：
TOKYO METOROPOLITAN UNIVERSITY
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
1997
资助国家：
日本
起止时间：
1997 至 1999
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-09640469/
关键词：
Ising Model percolation finite size scaling Monte Carlo method phase separation shear flow ポッツモデル

项目摘要

Effects of randomness on phase transitions and critical phenomena are interesting subjects of study. The purpose of the present research project is to investigate random spin systems by using Monte Carlo simulations. We have studied the relation between the phase transition of spin systems and geometric percolation transition, the finite-size scaling (FSS) of spin systems with anisotropic shape, and the phase separation dynamics of complex systems.First, based on the connection between the phase transition of the Ising model and the geometric percolation problem, we have studied the importance of the multiple percolating clusters for anisotropic Ising models. We have applied this idea to the random diluted Ising model, and discussed the crossover from the percolation fixed point to the thermal fixed point.Second, we have investigated the FSS functions for anisotropic Ising models. The anisotropic parameter dependence of FSS functions has been studied. For the anisotropic three-dimensional Ising models, we have obtained a unified view of three-dimensional and two-dimensional FSS, from the analysis of the FSS near the critical temperature of the layered Ising model.Third, we have investigated the phase separation dynamics under shear flow. Developing a new Monte Carlo method to study the phase separation under shear flow based on the spin model of the Kawasaki dynamics, we have discussed the anisotropic growth exponents in the late stage.

随机性对相变和关键现象的影响是有趣的研究主题。本研究项目的目的是使用蒙特卡洛模拟研究随机自旋系统。我们已经研究了自旋系统的相变与几何渗透过渡，具有各向异性形状的自旋系统的有限尺寸缩放（FSS），以及复杂系统的相位分离动力学。首先，基于ISING模型的相位过渡与几何模型的相关模型，我们已经对多种模型进行了验证，我们已经对多个模型进行了研究。我们已经将该想法应用于随机稀释的ISING模型，并讨论了从渗透固定点到热固定点的交叉。第二，我们研究了各向异性ISING模型的FSS函数。已经研究了FSS函数的各向异性参数依赖性。对于各向异性的三维ISING模型，我们从对分层ISING模型的临界温度附近的FSS分析中获得了三维和二维FSS的统一视图。我们研究了剪切流下的相位分离动力学。开发一种新的蒙特卡洛方法，根据川崎动力学的自旋模型研究剪切流下的相分离，我们已经讨论了晚期的各向异性生长指数。