  Here we report a precise computer simulation study of the static critical
properties of the two-dimensional $q$-states Potts model using very accurate
data obtained from a modified Wang-Landau (WL) scheme proposed by Caparica and
Cunha-Netto [Phys. Rev. E {\bf 85}, 046702 (2012)]. This algorithm is an
extension of the conventional WL sampling, but the authors changed the
criterion to update the density of states during the random walk and
established a new procedure to windup the simulation run. These few changes
have allowed a more precise microcanonical averaging which is essential to a
reliable finite-size scaling analysis. In this work we used this new technique
to determine the static critical exponents $\beta$, $\gamma$, and $\nu$, in an
unambiguous fashion. The static critical exponents were determined as
$\beta=0.10807(28)$, $\gamma=1.44716(72)$, and $\nu=0.818892(58)$, for the
$q=3$ case, and $\beta=0.09123(48)$, $\gamma=1.2855(13)$, and
$\nu=0.70640(10)$, for the $q=4$ Potts model. A comparison of the present
results with conjectured values and with those obtained from other well
established approaches strengthens this new way of performing WL simulations.
