  In this work we propose a criterion to finish the simulations of the
Wang-Landau sampling. Instead of determining a final modification factor for
all simulations and every sample sizes, we investigate the behavior of the
temperature of the peak of the specific heat during the simulations and finish
them when this value varies bellow a given limit. As a result, different runs
stop at different final modification factors. We show that in place of the
temperature of the peak of the specific heat one can adopt alternatively the
integrated heat transfer as a reference quantity. We apply this technique to
the two-dimensional Ising model and a homopolymer. We verify that for the Ising
model the mean order of the final modification factors are roughly the same for
all lattice sizes, but for the homopolymer the order of the final modification
factors increases with increasing polymer sizes. The results show that the
simulations can be halted much earlier then it is conventional in Wang-Landau
sampling, but manifold finite-size simulations are required in order to obtain
accurate results. A brief application to the three-dimensional Ising model is
also available.
