Studies on Mechanisms of Hierarchical Relaxation in Spin Glasses

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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