Exchange Monte Carlo Method and Application to Spin Glass Simulations

TL;DR

This paper introduces an exchange Monte Carlo algorithm that enhances the simulation efficiency of spin glass systems by enabling rapid relaxation and escape from local minima, outperforming traditional methods.

Contribution

The paper presents a novel exchange Monte Carlo method for simulating spin glasses, significantly reducing ergodicity time compared to existing approaches.

Findings

Ergodicity time is much smaller than in multi-canonical methods.

System relaxation is rapid, with exponential decay of correlation functions.

Relaxation times at low temperatures are comparable to ergodicity times.

Abstract

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