Large scale numerical simulation of the three-state Potts model

TL;DR

This paper uses large-scale numerical simulations to study the three-state Potts model on 3D lattices, revealing how long-range interactions cause weak first-order phase transitions by allowing disordered domain admixture.

Contribution

It provides new insights into the nature of phase transitions in the three-state Potts model, especially the role of long-range attraction in weakening the transition.

Findings

Disordered domains are induced by long-range attraction.

Weak first-order phase transitions are explained by domain admixture.

Numerical results on large lattices support the theoretical explanation.

Abstract

The three-state Potts model is numerically investigated on three-dimensional simple cubic lattices of up to \(128^3\) volume, concentrating on the neighborhood of the first-order phase transition separating the ordered and disordered phases. The ordered phase is found to allow admixture of disordered domains induced by a long-range attraction acting between the two different non-favored spins. This phenomenon gives an explanation of why the first-order phase transitions associated with the global \(Z_3\) symmetry are so weak. (Talk given at the International Symposium "Lattice 92" in Amsterdam, September 15-19, 1992)