Flat-histogram method comparison on the two-dimensional Ising model

Abstract

We compare the convergence of several flat-histogram methods applied to the two-dimensional Ising model, including the recently introduced stochastic approximation with a dynamic update factor (SAD) method. We compare this method to 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. We find that WL followed by a production run 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 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.