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

TL;DR

This study uses an improved Wang-Landau simulation method to accurately determine the static critical exponents of the two-dimensional q-states Potts model, providing more reliable finite-size scaling analysis.

Contribution

The paper introduces a modified Wang-Landau algorithm that enhances microcanonical averaging for precise critical exponent estimation in the Potts model.

Findings

Critical exponents for q=3: β=0.10807(28), γ=1.44716(72), ν=0.818892(58)

Critical exponents for q=4: β=0.09123(48), γ=1.2855(13), ν=0.70640(10)

Results agree with conjectured values and other methods.

Abstract

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.