| Research Abstract |
In the study of random systems, or complex systems, we often suffer from the problems of long time scales, or the problem of slow dynamics, which make computer simulation difficult. It is an urgent task to elucidate the nature of the slow dynamics, and to develop a novel simulation algorithm to conquer the problem of slow dynamics. The purpose of the present research is to study the dynamics in phase transitions by means of simulation methods such as Monte Carlo simulations.
In the present research project, we developed a new cluster algorithm to determine the critical point automatically, which is called the probability-changing cluster (PCC) algorithm. Applying this algorithm, we elucidated the crossover and self-averaging properties of two-dimensional (2D) random spin systems. We also applied the PCC algorithm to the 2D XY model, which shows the Kosterlitz-Thouless (KT) transition. Moreover, we generalized the PCC algorithms based on the finite-size scaling properties of the ratio of the correlation functions. With this generalized scheme, we studied the 2D quantum XY model of spin 1/2 to determine the KT transition point accurately.
We also proposed a new Monte Carlo dynamics, which combines the cluster algorithm and the extended ensemble method. This algorithm, which is based on the broad histogram relation, can be used as a Monte Carlo dynamics as well as the precise calculation of density of states. We showed the efficiency of this method for the Potts models.
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