Convergence of Stochastic Approximation Monte Carlo and modified Wang-Landau algorithms: Tests for the Ising model

摘要

We investigate the behavior of the deviation of the estimator for the densityof states (DOS) with respect to the exact solution in the course of Wang-Landauand Stochastic Approximation Monte Carlo (SAMC) simulations of thetwo-dimensional Ising model. We find that the deviation saturates in theWang-Landau case. This can be cured by adjusting the refinement scheme. To thisend, the 1/t-modification of the Wang-Landau algorithm has been suggested. Asimilar choice of refinement scheme is employed in the SAMC algorithm. Theconvergence behavior of all three algorithms is examined. It turns out that theconvergence of the SAMC algorithm is very sensitive to the onset of therefinement. Finally, the internal energy and specific heat of the Ising modelare calculated from the SAMC DOS and compared to exact values.