Wang-Landau sampling: Improving accuracy

In this work we investigate the behavior of the microcanonical and canonical averages of the two-dimensional Ising model during the Wang-Landau simulation. The simulations were carried out using conventional Wang-Landau sampling and the $1/t$ scheme. Our findings reveal that the microcanonical average should not be accumulated during the initial modification factors \textit{f} and outline a criterion to define this limit. We show that updating the density of states only after every $L^2$ spin-flip trials leads to a much better precision. We present a mechanism to determine for the given model up to what final modification factor the simulations should be carried out. Altogether these small adjustments lead to an improved procedure for simulations with much more reliable results. We compare our results with $1/t$ simulations. We also present an application of the procedure to a self-avoiding homopolymer.