Exchange Monte Carlo Method and Application to Spin Glass Simulations

Abstract

We propose an efficient Monte Carlo algorithm for simulating a\n``hardly-relaxing" system, in which many replicas with different temperatures\nare simultaneously simulated and a virtual process exchanging configurations of\nthese replica is introduced. This exchange process is expected to let the\nsystem at low temperatures escape from a local minimum. By using this algorithm\nthe three-dimensional $\\pm J$ Ising spin glass model is studied. The ergodicity\ntime in this method is found much smaller than that of the multi-canonical\nmethod. In particular the time correlation function almost follows an\nexponential decay whose relaxation time is comparable to the ergodicity time at\nlow temperatures. It suggests that the system relaxes very rapidly through the\nexchange process even in the low temperature phase.\n