Optimal modification factor and convergence of the Wang-Landau algorithm

We propose a strategy to achieve the fastest convergence in the Wang-Landau algorithm with varying modification factors. With this strategy, the convergence of a simulation is at least as good as the conventional Monte Carlo algorithm, i.e., the statistical error vanishes as 1/ root t, where t is a normalized time of the simulation. However, we also prove that the error cannot vanish faster than 1/t. Our findings are consistent with the 1/t Wang- Landau algorithm discovered recently, and we argue that one needs external information in the simulation to beat the conventional Monte Carlo algorithm.