The Critical Behaviour of Potts models with symmetry breaking fields

TL;DR

This paper investigates the critical behavior of two-dimensional Q-state Potts models under external magnetic fields, revealing how symmetry breaking influences phase transitions and multicritical points, supported by finite-size scaling, conformal invariance, and Monte Carlo simulations.

Contribution

It introduces a detailed analysis of symmetry-breaking effects on Potts models, identifying conditions for multicritical points and employing multiple methods for validation.

Findings

Multicritical points occur at zero field for models with Z(Q') symmetry, Q' ≤ 4.

Effective models with smaller symmetry groups are obtained through specific magnetic fields.

Monte Carlo simulations support the theoretical predictions.

Abstract

The $Q$-state Potts model in two dimensions in the presence of external magnetic fields is studied. For general $Q\geq3$ special choices of these magnetic fields produce effective models with smaller $Z(Q')$ symmetry $(Q'< Q)$. The phase diagram of these models and their critical behaviour are explored by conventional finite-size scaling and conformal invariance. The possibility of multicritical behavior, for finite values of the symmetry breaking fields, in the cases where $Q>4$ is also analysed. Our results indicate that for effective models with $Z(Q')$ symmetry $(Q'\leq4)$ the multicritical point occurs at zero field. This last result is also corroborated by Monte Carlo simulations.