Wang-Landau sampling: a criterion for halting the simulations

TL;DR

This paper introduces a new criterion based on the specific heat peak behavior to determine when to stop Wang-Landau sampling simulations, allowing for earlier termination and potentially more efficient computations.

Contribution

It proposes a novel stopping criterion for Wang-Landau sampling based on the temperature of the specific heat peak or integrated heat transfer, tested on various models.

Findings

Simulations can be halted earlier than traditional methods.

The final modification factors are consistent across lattice sizes for the Ising model.

The method's effectiveness varies with system size, especially for polymers.

Abstract

In this work we propose a criterion to finish the simulations of the Wang-Landau sampling. Instead of determining a final modification factor for all simulations and every sample sizes, we investigate the behavior of the temperature of the peak of the specific heat during the simulations and finish them when this value varies bellow a given limit. As a result, different runs stop at different final modification factors. We show that in place of the temperature of the peak of the specific heat one can adopt alternatively the integrated heat transfer as a reference quantity. We apply this technique to the two-dimensional Ising model and a homopolymer. We verify that for the Ising model the mean order of the final modification factors are roughly the same for all lattice sizes, but for the homopolymer the order of the final modification factors increases with increasing polymer sizes. The results show that the simulations can be halted much earlier then it is conventional in Wang-Landau sampling, but manifold finite-size simulations are required in order to obtain accurate results. A brief application to the three-dimensional Ising model is also available.