Numerical Analysis of the Clister Effect in Spin Glass Systems

在自旋玻璃等随机受挫系统中存在许多亚稳态。考虑到这种情况，人们预计大多数这样的系统都表现出玻璃般的弛豫，事实上，在许多材料中已经在实验中发现了极慢的动力学。理解反常弛豫的一个想法是，自旋彼此高度相关的星团的产生和增长。这项研究的目的是揭示团簇的行为以及它们与反常弛豫的关系。我们的研究安排如下：1.为了了解反常弛豫是如何从高温发展而来的，我们用蒙特卡罗模拟方法研究了J-Ising自旋Edwards-Anderson模型的自关联函数Q(T)，发现在观察到拉伸的指数弛豫时存在着与Griffith相的交叉。2.在蒙特卡罗模拟中，慢弛豫阻碍了我们研究系统的平衡态。我们提出了一种新的算法，称为副本交换方法，它缩短了松弛时间以达到受挫系统的平衡，并证明了它在研究自旋玻璃系统中也是有效的。3.利用上述方法，我们将观察两点关联函数来确定(]sy.+-.]J Ising模型的团簇，并澄清与Griffith相的关系。不幸的是，我们还没有完成这项分析，它仍然是我们在未来的项目中必须完成的工作。

There exist many metastable states in randomly frustrated systems such as spin glass. Considering the situation, one expects that most of such systems exhibit glassy relaxations, and in fact, extremely slow dynamics has been found experimentally in many materials. One of the ideas to understand the anomalous relaxation is creation andgrowth of clusters in which spins are highly correlated with each other. The purpose of this research was to reveal how the clusters behaves and how they relate to the anomalous relaxation. Our research was organized as follows :1.In order to understand how the anomalous relaxation develops from high temperatures, we have investigated the autocorrelation function q(t) of the (]SY.+-.])J Ising spin Edwards-Anderson model by Monte Carlo simulation, and found the cross-over to the Griffith phase in observing the stretched exponential relaxation.2.In Monte Carlo simulation, the slow relaxation prevents us from investigating equilibrium state of the system. We have proposed a new algorithm, called the replica-exchange method, which diminishes relaxation time to reach equilibrium of the frustrated system, and have shown that it works effectively in studying the spin glass system as well.3.Using the above method, we are going to observe the 2 point correlation function to determine the clusters of the (]SY.+-.])J Ising model and to clarify the relation to the Griffith phase. Unfortunately we have not yet completed this analysis and it remains as what we have to finish in a future project.