Monte Carlo Simulation of Quantum and Random Spin Systems

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的蒙特卡罗模拟，以获得关于量子和随机自旋系统的准确的数值信息。在这里，我们从几个主题集中讨论了三个主题。首先，我们研究了普适有限尺寸标度问题。我们已经证明了这个概念可以应用于二维伊辛模型，其中我们特别注意了边界条件。特别研究了具有倾斜边界条件的矩形晶格的有限尺寸标度问题。其次，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化动力学。我们观察到，即使在深度淬火的情况下，磁畴也在低温下迅速长大，并且发现磁畴的长大受指数为1/3的简单代数生长规律的控制。第三，我们发展了一种新的快速模拟方法，利用自旋模型来研究剪切流下的相分离。它使我们能够研究热涨落对相分离的影响，而这是传统的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。

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.