Wang-Landau sampling: Improving accuracy

TL;DR

This paper enhances Wang-Landau sampling accuracy by proposing new guidelines for averaging and updating the density of states, leading to more reliable results in Ising model simulations and polymer applications.

Contribution

It introduces improved criteria for averaging and updating in Wang-Landau sampling, significantly increasing simulation precision and reliability.

Findings

Microcanonical averages should not be accumulated during initial modification factors.

Updating density of states after every $L^2$ trials improves accuracy.

The proposed method yields more reliable results compared to traditional $1/t$ schemes.

Abstract

In this work we investigate the behavior of the microcanonical and canonical averages of the two-dimensional Ising model during the Wang-Landau simulation. The simulations were carried out using conventional Wang-Landau sampling and the $1/t$ scheme. Our findings reveal that the microcanonical average should not be accumulated during the initial modification factors \textit{f} and outline a criterion to define this limit. We show that updating the density of states only after every $L^2$ spin-flip trials leads to a much better precision. We present a mechanism to determine for the given model up to what final modification factor the simulations should be carried out. Altogether these small adjustments lead to an improved procedure for simulations with much more reliable results. We compare our results with $1/t$ simulations. We also present an application of the procedure to a self-avoiding homopolymer.