Non compact continuum limit of two coupled Potts models

TL;DR

This paper investigates the continuum limit of two coupled Potts models with relevant interactions, revealing a complex structure involving compact and non-compact bosons, and providing corrected critical exponents and magnetic scaling dimensions.

Contribution

It establishes a link between coupled Potts models and an integrable vertex model, deriving Bethe Ansatz equations, and characterizes the continuum limit with detailed bosonic field content and corrected critical exponents.

Findings

Continuum limit involves two compact and one non-compact bosons.

Discrete states emerge from the continuum at specific twists.

Corrected critical exponents and magnetic scaling dimensions for the Potts model.

Abstract

We study two $Q$-state Potts models coupled by the product of their energy operators, in the regime $2 < Q \le 4$ where the coupling is relevant. A particular choice of weights on the square lattice is shown to be equivalent to the integrable $a_3^{(2)}$ vertex model. It corresponds to a selfdual system of two antiferromagnetic Potts models, coupled ferromagnetically. We derive the Bethe Ansatz equations and study them numerically for two arbitrary twist angles. The continuum limit is shown to involve two compact bosons and one non compact boson, with discrete states emerging from the continuum at appropriate twists. The non compact boson entails strong logarithmic corrections to the finite-size behaviour of the scaling levels, the understanding of which allows us to correct an earlier proposal for some of the critical exponents. In particular, we infer the full set of magnetic scaling dimensions (watermelon operators) of the Potts model.