Three-State Anti-ferromagnetic Potts Model in Three Dimensions: Universality and Critical Amplitudes

TL;DR

This study uses Monte Carlo simulations to analyze the critical behavior of the three-dimensional anti-ferromagnetic 3-state Potts model, confirming its universality class and providing precise critical parameters.

Contribution

It provides the first detailed Monte Carlo analysis of the 3D anti-ferromagnetic 3-state Potts model, establishing its universality class and accurately estimating critical parameters.

Findings

Critical coupling $eta_c=0.81563(3)$

Critical exponents $rac{eta}{ u}=1.973(9)$ and $ u=0.664(4)$

Supports universality with the 3D XY model

Abstract

We present the results of a Monte Carlo study of the three-dimensional anti-ferromagnetic 3-state Potts model. We compute various cumulants in the neighbourhood of the critical coupling. The comparison of the results with a recent high statistics study of the 3D XY model strongly supports the hypothesis that both models belong to the same universality class. From our numerical data for the anti-ferromagnetic 3-state Potts model we obtain for the critical coupling $\coup_c=0.81563(3)$, and for the static critical exponents $\gamma /\nu=1.973(9)$ and $\nu=0.664(4)$.