Critical points in coupled Potts models and critical phases in coupled loop models

TL;DR

This paper introduces a method to couple two critical Potts models to create a new self-dual critical point and identifies a dense critical phase, supported by exact results and numerical analysis.

Contribution

It demonstrates how to couple two critical Potts models to produce a novel self-dual critical point and characterizes the associated dense critical phase using conformal field theory and numerical methods.

Findings

Identification of a new self-dual critical point in coupled Potts models

Evidence of a dense critical phase near the critical point in loop representations

Phase diagram including effects of vacancies and different Q values

Abstract

We show how to couple two critical Q-state Potts models to yield a new self-dual critical point. We also present strong evidence of a dense critical phase near this critical point when the Potts models are defined in their completely packed loop representations. In the continuum limit, the new critical point is described by an SU(2) coset conformal field theory, while in this limit of the the critical phase, the two loop models decouple. Using a combination of exact results and numerics, we also obtain the phase diagram in the presence of vacancies. We generalize these results to coupling two Potts models at different Q.