Flat histogram method comparison on 2D Ising Model

Abstract

We compare the convergence of several flat-histogram methods applied to the 2D Ising model, including the recently introduced stochastic approximation with a dynamic update factor (SAD) method. We compare this method with the Wang-Landau (WL) method, the $1/t$ variant of the WL method, and standard stochastic approximation Monte Carlo (SAMC). In addition, we consider a procedure WL followed by a "production run" with fixed weights that refines the estimation of the entropy. To our knowledge, this work is the first to test this approach against other methods. We find that WL followed by a production run \emph{does} converge to the true density of states, in contrast to pure WL. Three of the methods converge robustly: SAD, $1/t$-WL, and WL followed by a production run. Of these, SAD does not require \emph{a priori} knowledge of the energy range. This work also shows that WL followed by a production run performs superior to other forms of WL while ensuring both ergodicity and detailed balance.

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