Accuracy and convergence of the Wang-Landau sampling algorithm

We present estimations of the accuracy and convergence of the Wang-Landau algorithm. Both accuracy and the related length of the Monte Carlo run depend on the modification parameter f and the density of states. The analytical solution obtained for the two-level system was checked numerically on the two-dimensional Ising model. Although the two-level system is a very simple one, it appears that the proposed solution describes the generic features of the Wang-Landau algorithm. The estimations should prove useful in Monte Carlo calculations of protein folding, first-order transitions, and other systems with a rough energy landscape.