The Behavior of the Three-Dimensional Askin–Teller Model at the Mixed Phase Region by a New Monte Carlo Approach

Abstract

The new approach of performing Monte Carlo (MC) simulations, which eliminates large oscillations of the values of the thermodynamic quantities computed for a mixed phase region, is demonstrated. The results are presented on the example of the mixed phase region in the 3D Askin–Teller (AT) model, where within a certain range of parameters with equal probabilities there appear two different, but equivalent, ways of ordering two of the three order parameters showing independent behavior. This new approach allowed us to exploit magnetization and internal energy curves, Binder cumulant, Challa- and the Lee-Kosterlitz-like cumulants as well as the internal energy distribution histogram. According to the most effective strategy, in the critical region, we use our recently proposed cluster MC algorithm and the Metropolis algorithm beyond it wherever it is applicable. The existence of two tricritical points and the bifurcation point in this area of the phase diagram is confirmed, and their locations are determined. It is explained that although the system as a whole does not show the presence of latent heat at the boundary of the mixed phase region and the antiferromagnetic phase, it does occur for various order parameters. Specifically, the increase in the energy of the degrees of freedom of one kind is accompanied by an equal decrease in the energy of the degrees of freedom of the other kind.