  In this work, we present a comparative study of the accuracy provided by the
Wang-Landau sampling and the Broad Histogram method to estimate de density of
states of the two dimensional Ising ferromagnet. The microcanonical averages
used to describe the thermodynamic behaviour and to use the Broad Histogram
method were obtained using the single spin-flip Wang-Landau sampling,
attempting to convergence issues and accuracy improvements. We compare the
results provided by both techniques with the exact ones for thermodynamic
properties and critical exponents. Our results, within the Wang-Landau
sampling, reveal that the Broad Histogram approach provides a better
description of the density of states for all cases analysed.
