A List Referring Monte-Carlo Method for Lattice Glass Models

Abstract

We present an effcient Monte-Carlo method for lattice glass models which are characterized by hard constraint conditions. The basic idea of the method is similar to that of the $N$-fold way method. By using a list of sites into which we can insert a particle, we avoid trying a useless transition which is forbidden by the constraint conditions. We applied the present method to a lattice glass model proposed by Biroli and M{\'e}zard. We first evaluated the efficiency of the method through measurements of the autocorrelation function of particle configurations. As a result, we found that the efficiency is much higher than that of the standard Monte-Carlo method. We also compared the efficiency of the present method with that of the $N$-fold way method in detail. We next examined how the efficiency of extended ensemble methods such as the replica exchange method and the Wang-Landau method is inflnuenced by the choice of the local update method. The results show that the efficiency is considerably improved by the use of efficient local update methods. For example, when the number of sites $N_{\rm site}$ is 1024, the ergodic time $\tau_{\rm E}$ of the replica exchange method in the grand-canonical ensemble, which is the average round-trip time of a replica in chemical-potential space, with the present local update method is more than $10^2$ times shorter than that with the standard local update method. This result shows that the efficient local update method is quite important to make extended ensemble methods more effective.