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Here we report a precise computer simulation study of the static criticalproperties of the two-dimensional $q$-states Potts model using very accuratedata obtained from a modified Wang-Landau (WL) scheme proposed by Caparica andCunha-Netto [Phys. Rev. E {\bf 85}, 046702 (2012)]. This algorithm is anextension of the conventional WL sampling, but the authors changed thecriterion to update the density of states during the random walk andestablished a new procedure to windup the simulation run. These few changeshave allowed a more precise microcanonical averaging which is essential to areliable finite-size scaling analysis. In this work we used this new techniqueto determine the static critical exponents $\beta$, $\gamma$, and $\nu$, in anunambiguous 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 presentresults with conjectured values and with those obtained from other wellestablished approaches strengthens this new way of performing WL simulations.

Static critical behavior of the $q-$states Potts model: High-resolution entropic study