Universal ratios of critical amplitudes in the Potts model universality class

TL;DR

This study uses Monte Carlo simulations and series expansions to analyze universal amplitude ratios near critical points in the Potts and Baxter-Wu models, confirming their shared universality class despite logarithmic corrections.

Contribution

It provides analytical and numerical evidence that the four-state Potts and Baxter-Wu models share the same universality class, including relations among correction-to-scaling amplitudes.

Findings

Universal amplitude ratios are consistent across models.

Effective ratios approach unity linearly near criticality.

Critical behavior of both models is governed by the same fixed point.

Abstract

Monte Carlo (MC) simulations and series expansions (SE) data for the energy, specific heat, magnetization, and susceptibility of the three-state and four-state Potts model and Baxter-Wu model on the square lattice are analyzed in the vicinity of the critical point in order to estimate universal combinations of critical amplitudes. We also form effective ratios of the observables close to the critical point and analyze how they approach the universal critical-amplitude ratios. In particular, using the duality relation, we show analytically that for the Potts model with a number of states $q\le 4$, the effective ratio of the energy critical amplitudes always approaches unity linearly with respect to the reduced temperature. This fact leads to the prediction of relations among the amplitudes of correction-to-scaling terms of the specific heat in the low- and high-temperature phases. It is a common belief that the four-state Potts and the Baxter-Wu model belong to the same universality class. At the same time, the critical behavior of the four-state Potts model is modified by logarithmic corrections while that of the Baxter-Wu model is not. Numerical analysis shows that critical amplitude ratios are very close for both models and, therefore, gives support to the hypothesis that the critical behavior of both systems is described by the same renormalization group fixed point.