Wang-Landau/Multibondic Cluster Simulations for Second-Order Phase Transitions

TL;DR

This paper introduces a cluster-based Wang-Landau and multibondic simulation method that significantly enhances efficiency for studying second-order phase transitions in Ising models, reducing CPU time by two orders of magnitude.

Contribution

A novel cluster algorithm implementation of Wang-Landau recursion combined with multibondic simulation for improved efficiency in phase transition studies.

Findings

Efficiency improved by power laws in lattice size

CPU time reduced by two orders of magnitude

Effective for 2D and 3D Ising models

Abstract

For a second-order phase transition the critical energy range of interest is larger than the energy range covered by a canonical Monte Carlo simulation at the critical temperature. Such an extended energy range can be covered by performing a Wang-Landau recursion for the spectral density followed by a multicanonical simulation with fixed weights. But in the conventional approach one loses the advantage due to cluster algorithms. A cluster version of the Wang-Landau recursion together with a subsequent multibondic simulation improves for 2D and 3D Ising models the efficiency of the conventional Wang-Landau/multicanonical approach by power laws in the lattice size. In our simulations real gains in CPU time reach two orders of magnitude.