Energy degeneracies from Broad Histogram Method and Wang-Landau Sampling

TL;DR

This paper compares Wang-Landau sampling and the Broad Histogram method in estimating the density of states for the 2D Ising model, finding the Broad Histogram approach generally more accurate.

Contribution

It provides a comparative analysis of two methods for density of states estimation, highlighting the superior accuracy of the Broad Histogram method in this context.

Findings

Broad Histogram method yields more accurate density of states estimates.

Wang-Landau sampling shows convergence issues but is useful for microcanonical averages.

Results agree with exact thermodynamic properties and critical exponents.

Abstract

In this work, we present a comparative study of the accuracy provided by the Wang-Landau sampling and the Broad Histogram method to estimate de density of states of the two dimensional Ising ferromagnet. The microcanonical averages used to describe the thermodynamic behaviour and to use the Broad Histogram method were obtained using the single spin-flip Wang-Landau sampling, attempting to convergence issues and accuracy improvements. We compare the results provided by both techniques with the exact ones for thermodynamic properties and critical exponents. Our results, within the Wang-Landau sampling, reveal that the Broad Histogram approach provides a better description of the density of states for all cases analysed.