Title: Convergence of Stochastic Approximation Monte Carlo and modified Wang-Landau algorithms: Tests for the Ising model,
Abstract: We investigate the behavior of the deviation of the estimator for the density
of states (DOS) with respect to the exact solution in the course of Wang-Landau
and Stochastic Approximation Monte Carlo (SAMC) simulations of the
two-dimensional Ising model. We find that the deviation saturates in the
Wang-Landau case. This can be cured by adjusting the refinement scheme. To this
end, the 1/t-modification of the Wang-Landau algorithm has been suggested. A
similar choice of refinement scheme is employed in the SAMC algorithm. The
convergence behavior of all three algorithms is examined. It turns out that the
convergence of the SAMC algorithm is very sensitive to the onset of the
refinement. Finally, the internal energy and specific heat of the Ising model
are calculated from the SAMC DOS and compared to exact values.