Determination of the dynamic and static critical exponents of the two-dimensional three-state Potts model using linearly varying temperature

Abstract

We employ a successive Monte Carlo renormalization group procedure in the presence of a linearly varying temperature to study the three-state (q=3) Potts model on square lattices. By matching correlation functions of different lattice sizes at different renormalization levels, a rate exponent r associated with the temperature sweep rate R and the correlation length exponent nu are obtained. The dynamic critical exponent z is then obtained by the scaling law z=r-1/nu derived in our method. The results of z=2.171(62) for q=3 in this work and the previously obtained z=2.15(13) for q=2 seem to support the extension of the "weak universality" hypothesis to dynamic critical behavior. With these calculated exponents, the dynamic scaling forms of both specific heat and order parameter at various R are presented and all the other static critical exponents are determined, which verify our method. Discussions are made on how to improve the accuracy of the estimation of the dynamic critical exponent.