Static critical behavior of the \(q-\)states Potts model: High-resolution entropic study

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.