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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.

随机性对相变和临界现象的影响是有趣的研究课题。本研究的目的是用蒙特卡罗模拟方法研究随机自旋系统。我们研究了自旋系统的相变与几何渗流相变、各向异性形状自旋系统的有限尺寸标度(FSS)以及复杂系统的相分离动力学之间的关系。首先，基于伊辛模型的相变与几何渗流问题之间的联系，我们研究了多个渗流团簇对各向异性伊辛模型的重要性。我们将这一思想应用到随机稀释伊辛模型中，讨论了从渗流不动点到热不动点的交叉。其次，我们研究了各向异性伊辛模型的FSS函数。研究了FSS函数的各向异性参数依赖性。对于各向异性三维伊辛模型，通过对分层伊辛模型临界温度附近的相分离的分析，得到了三维和二维相分离的统一视图。第三，我们研究了剪切流作用下的相分离动力学。基于川崎动力学的自旋模型，发展了一种新的蒙特卡罗方法来研究剪切流作用下的相分离，讨论了后期的各向异性生长指数。