Munetaka Sasaki, Koji Hukushima
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. Since it is a waste of computational time trying an insertion of a particle which is forbidden by constraint conditions, we just try an insertion which does not conflict with the constraint conditions by using a list of the insertable sites. The list is made at the beginning of the simulation, and it is updated whenever the particle configuration is changed. We applied the method to a lattice glass model proposed by Biroli and M\'ezard. We first evaluated the efficiency of the method through measurements of the autocorrelation function of particle configurations. As a result, we found that, when the chemical potential $\mu$ is large, the relaxation time of the present method is about $10^3$ times shorter than that of the standard Monte Carlo method. This result shows that the efficiency of simulations is much improved, even given the computational cost to keep the list of the insertable sites. We next examined how the efficiency of the replica exchange method concerning chemical potential is influenced by a choise of a local update method. The results show that the efficiency of the replica exchange method is considerably improved by the use of the proposed update method. For example, when $N_{\rm site}=1024$, the ergodic time $\tau_{\rm E}$, 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. Lastly, we calculated the density of states of the model by combining the present method with the Wang-Landau method.
View original:
http://arxiv.org/abs/1207.7189
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