Universal ratios of critical amplitudes in the Potts model universality class
Abstract
Monte Carlo (MC) simulations and series expansions (SE) data for the energy, specific heat, magnetization, and susceptibility of the threestate and fourstate Potts model and the BaxterWu 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 criticalamplitude ratios. In particular, using the duality relation, we show analytically that for the Potts model with a number of states q⩽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 correctiontoscaling terms of the specific heat in the low and hightemperature phases. It is a common belief that the fourstate Potts and the BaxterWu model belong to the same universality class. At the same time, the critical behavior of the fourstate Potts model is modified by logarithmic corrections while that of the BaxterWu 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.
 Publication:

Computer Physics Communications
 Pub Date:
 April 2009
 DOI:
 10.1016/j.cpc.2008.12.022
 arXiv:
 arXiv:0809.5045
 Bibcode:
 2009CoPhC.180..493B
 Keywords:

 0.50.+q;
 75.10.b;
 General theory and models of magnetic ordering;
 Condensed Matter  Statistical Mechanics;
 Astrophysics;
 High Energy Physics  Lattice
 EPrint:
 Talk presented at CCP 2008, Ouro Preto, 59 August 2008