Field theory of scaling lattice models. The Potts antiferromagnet

TL;DR

This paper explores how lattice structure influences critical behavior in antiferromagnetic systems, specifically analyzing the square lattice three-state Potts model and its description via sine-Gordon field theory.

Contribution

It demonstrates that the lattice structure's influence persists in the field theory description of the antiferromagnetic Potts model and introduces a field theory for the crossover to ferromagnetic behavior.

Findings

The antiferromagnetic Potts model at T->0 is described by sine-Gordon theory.

Lattice effects are retained in the continuum field theory.

A field theory for the antiferromagnetic to ferromagnetic crossover is proposed.

Abstract

In contrast to what happens for ferromagnets, the lattice structure participates in a crucial way to determine existence and type of critical behaviour in antiferromagnetic systems. It is an interesting question to investigate how the memory of the lattice survives in the field theory describing a scaling antiferromagnet. We discuss this issue for the square lattice three-state Potts model, whose scaling limit as T->0 is argued to be described exactly by the sine-Gordon field theory at a specific value of the coupling. The solution of the scaling ferromagnetic case is recalled for comparison. The field theory describing the crossover from antiferromagnetic to ferromagnetic behaviour is also introduced.