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

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.

Stochastic approximation Monte Carlo with a dynamic update factor.

We present a Monte Carlo algorithm based on the stochastic approximation Monte Carlo (SAMC) algorithm for directly calculating the density of states. The proposed method is stochastic approximation with a dynamic update factor (SAD), which dynamically adjusts the update factor γ_{t} during the course of the simulation. We test this method on a square-well fluid and a 31-atom Lennard-Jones cluster and compare the convergence behavior of several related Monte Carlo methods.