Studies on Mechanisms of Hierarchical Relaxation in Spin Glasses

在自旋玻璃中，在转变温度T_C以下的有序相中存在自由能局域最小态的分层组织，在T_C以上的“格里菲斯相”中存在自旋团簇之一。在本项目中，我们通过蒙特卡罗模拟研究了自旋玻璃中与这种状态组织相关的层次松弛机制，并获得了以下结果。在分析三维Ising自旋玻璃（EA）模型在T_C以上的“Griffiths相位”中的弛豫过程中，我们利用最大熵法从模拟的自旋自相关函数中评估了自旋弛豫时间的分布函数。得到的分布清楚地揭示了两种松弛机制的共存；格里菲思相特有的簇弛豫和通常在连续相变附近出现的临界弛豫。在有限尺寸的SK模型中，研究了自旋玻璃在温度高于T_c到低于T_c的温度下，需要很长时间才能达到T的平衡，这种平衡过程称为时效。他们的模拟结果让我们对系统中的老化过程有了如下的设想。当淬火后的等待时间t_w过去后，系统处于自由能较高的局部极小值之一。在这个t_w的时间尺度内，系统在局部最小值（准平衡域）周围的有限区域内波动，并表现出类似平衡的性质，如满足波动耗散定理。当等待时间超过这个尺度时，通过热活化过程，系统寻找另一个自由能更低、准平衡域更大的局部最小值。这样，系统最终达到平衡。我们称之为“准平衡域的增长”情景。我们还研究了三维高斯EA模型中的老化现象。通过对能量弛豫过程和克隆相关函数的分析，我们证实了平衡域（在这个短程模型的实空间中）的增长在t_w中服从幂律，这一点已经通过分析自旋玻璃磁化率等其他量得到。少

In spin glasses there exit a hierarchical organization of the free-energy local-minimum states in the ordered phase below the transition temperature T_C, as well as the one of the spin clusters in the 'Griffiths phase' above T_C. In the present project we have investigated mechanisms of hierarchical relaxations associated with such organizations of states in spin glasses by means of Monte Carlro simulations, and have obtained the results described below.In the analysis of relaxation processes in the 3D Ising spin-glass (EA) models in their 'Griffiths phase' above T_C we have evaluated the distribution function of spin relaxation times from the simulated spin auto-correlation function by making use of the maximum entropy method. The obtained distribution reveals distinctly the co-existence of two relaxational mechanisms ; the cluster relaxation peculiar to the 'Griffiths phase' and the critical relaxation generally seen near a continuous phase transition.When a spin glass is quenched fr … More om above T_c to a certain temperature T below T_c, it takes so long time for it to reach equilibrium at T.This equilibration process, called aging, has been investigated in the SK model of finite sizes. They simulated results have led us to the following scenario for the aging process in the system. When the waiting time t_w has passed after the quench, the system is found in one of the free-energy local minima with a relatively higher free-energy. Within the time scale of this t_w, the system is fluctuating within a limited region around the local minimum (quasi-equilibrium domain) and exhibits equilibrium-like properties such as satisfaction of the fluctuation-dissipation theorem. When the waiting time exceeds this scale, by means of the thermal activation process, the system finds another local-minimum with a lower free-energy and with a larger quasi-equibrium domain. In this way the system reaches to equilibrium finally. We have called this the "Growth of Quasi-Equilibrium Domain" scenario.We have also examined aging phenomena in the 3D Gaussian EA model. Through analyzes on the relaxation process of energy as well as on the clone-correlation function, we have confirmed that growth of the equilibrium domain (in the real space in this short-ranged model) obeys a power law in t_w as already found through analysis on other quantities such as the spin-glass susceptibility. Less