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级结构，在T_C以上的“Griffiths相”中也存在自旋团簇的分级结构。在本项目中，我们研究了与自旋玻璃中的这种态组织相关的分级弛豫机制，在分析3D Ising自旋玻璃（EA）模型在T_C以上的“Griffiths相”中的弛豫过程时，我们从模拟的自旋自洽场计算了自旋弛豫时间的分布函数，利用最大熵方法建立相关函数。所得到的分布清楚地揭示了两种弛豫机制的共存：“Griffiths相”特有的团簇弛豫和通常在连续相变附近看到的临界弛豫。 ...更多信息 从T_c以上到T_c以下的某个温度T，需要很长的时间才能在T处达到平衡。他们的模拟结果使我们对系统中的老化过程产生了以下情景。当失超后等待时间t_w已过时，系统处于自由能相对较高的自由能局部极小点之一。在此时间尺度上，系统在局部极小值附近的有限区域（准平衡区域）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，通过热激活过程，系统找到另一个具有较低自由能和较大准等熵域的局部极小值。这样，系统最终达到平衡。我们称之为“准平衡域的增长”方案。我们还研究了3D高斯EA模型中的老化现象。通过对能量弛豫过程和克隆关联函数的分析，我们证实了平衡畴（在短程模型中是在真实的空间）的增长服从t_w的幂律，这一点已通过对自旋玻璃磁化率等其它物理量的分析得到。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