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Monte Carlo Simulation of Quantum and Random Spin Systems

量子和随机自旋系统的蒙特卡罗模拟

基本信息

批准号：
07640518
负责人：
OKABE Yutaka
金额：
$ 1.28万
依托单位：
TOKYO METROPOLITAN UNIVERSITY
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
1995
资助国家：
日本
起止时间：
1995 至 1996
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-07640518/
关键词：
finite size scaling Ising model ordering dynamics exchange Monte Carlo shear flow Kawasaki dynamics モンテカルロ法秩序形成ポッツモデルランダム磁場

项目摘要

The effect of randomness on phase transitions and critical phenomena is an interesting problem. The purpose of the present study is to perform massive Monte Carlo simulation for getting accurate numerical information on quantum and random spin systems. We here focus on three topics from several subjects.First, we have studied the problem of the universal finite-size scaling. We have shown that this concept can be applied to the two-dimensional Ising model, where we have paid special attention to the boundary conditions. Especially, we have studied the finite-size scaling of the rectangular lattice with tilted boundary conditions.Second, we have applied the exchange Monte Carlo method to the ordering dynamics of the three-component system with the conserved order parameter. We have observed a rapid domain growth even for the deeply quenched case to low temperatures, and have found that a domain growth is controlled by a simple algebraic growth law with the exponent 1/3.Third, we have developed a new fast simulation method to study phase separation under shear flow by using spin model. It enables us to study the effect of thermal fluctuation on phase separation which could not be studied by conventional simulation methods. We have also proposed a new method to analyze anisotropic temporal evolution of structure factor.

随机性对相变和临界现象的影响是一个有趣的问题。本研究的目的是对量子和随机自旋系统进行大量的蒙特卡罗模拟，以获得精确的数值信息。本文主要从三个方面进行研究：第一，研究了泛有限尺度问题。我们已经证明，这个概念可以应用到二维伊辛模型，在那里我们特别注意的边界条件。特别地，我们研究了具有倾斜边界条件的矩形格子的有限尺度标度。其次，我们将交换Monte Carlo方法应用于具有守恒序参量的三组分体系的有序动力学。我们观察到在低温下，即使在深度淬火的情况下，磁畴也会迅速长大，并且发现磁畴的长大受一个简单的代数增长规律控制，其指数为1/3。第三，我们发展了一种新的快速模拟方法，利用自旋模型研究剪切流下的相分离。这使得我们能够研究热涨落对相分离的影响，这是不能用传统的模拟方法研究。我们还提出了一种新的方法来分析各向异性的结构因子的时间演化。