Numerical Analysis of the Clister Effect in Spin Glass Systems

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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.