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。本研究的目的是进行大规模蒙特卡罗模拟，以获得有关量子和随机自旋系统的准确数值信息。我们在这里重点关注几个主题的三个主题。首先，我们研究了通用有限尺寸缩放问题。我们已经证明这个概念可以应用于二维伊辛模型，我们特别关注了边界条件。特别是，我们研究了具有倾斜边界条件的矩形晶格的有限尺寸缩放。其次，我们将交换蒙特卡罗方法应用于具有守恒序参数的三组分系统的有序动力学。即使在深度淬火的情况下，我们也观察到了域的快速生长，并且发现域的生长是由指数为 1/3 的简单代数生长定律控制的。第三，我们开发了一种新的快速模拟方法使用自旋模型研究剪切流下的相分离。它使我们能够研究热波动对相分离的影响，这是传统模拟方法无法研究的。我们还提出了一种分析结构因子各向异性时间演化的新方法。