Phase Diagram of the Square-Lattice Three-State Potts Antiferromagnet with Staggered Polarization Field

TL;DR

This paper investigates the phase diagram of a square-lattice three-state Potts antiferromagnet with a staggered polarization field, identifying phase boundaries and critical behaviors through numerical transfer matrix analysis.

Contribution

It provides the first detailed numerical determination of phase boundaries and confirms the nature of critical points, including a ferromagnetic Potts and an Ising transition, in this model.

Findings

Identified two phase boundaries with distinct critical behaviors.

Confirmed the ferromagnetic three-state Potts criticality.

Established the Ising-type transition and its field theory description.

Abstract

We study a square-lattice three-state Potts antiferromagnet with a staggered polarization field at finite temperature. Numerically treating the transfer matrices, we determine two phase boundaries separating the model-parameter space into three parts. We confirm that one of them belongs to the ferromagnetic three-state Potts criticality, which is in accord with a recent prediction, and another to the Ising type; these are both corresponding to the massless renormalization-group flows stemming from the Gaussian fixed points. We also discuss a field theory to describe the latter Ising transition.