Finite-temperature phase transition in a class of 4-state Potts antiferromagnets

TL;DR

This paper predicts and confirms a finite-temperature phase transition in certain 4-state Potts antiferromagnets on specific Eulerian plane triangulations, identifying its universality class through transfer-matrix and Monte Carlo methods.

Contribution

It introduces a new class of Eulerian plane triangulations where the 4-state Potts antiferromagnet exhibits a finite-temperature phase transition and determines its universality class.

Findings

Finite-temperature phase transition confirmed on union-jack and bisected hexagonal lattices.

Universality class of the transition predicted and validated.

Transfer-matrix and Monte Carlo data support theoretical predictions.

Abstract

We argue that the 4-state Potts antiferromagnet has a finite-temperature phase transition on any Eulerian plane triangulation in which one sublattice consists of vertices of degree 4. We furthermore predict the universality class of this transition. We then present transfer-matrix and Monte Carlo data confirming these predictions for the cases of the union-jack and bisected hexagonal lattices.