Integrable aspects of the scaling q-state Potts models II: finite-size effects

TL;DR

This paper investigates finite-size effects in q-state Potts models near critical points, providing TBA equations and analyzing flows between tricritical and critical models, with implications for off-critical dilute A models.

Contribution

It introduces TBA equations for finite-size analysis of q-state Potts models related to specific perturbations, extending previous infinite-line spectrum results.

Findings

TBA equations validated in ultraviolet and infrared limits

Analysis of flows from tricritical to critical models across q range

Relevance established for off-critical dilute A models

Abstract

We continue our discussion of the q-state Potts models for q <= 4, in the scaling regimes close to their critical and tricritical points. In a previous paper, the spectrum and full S-matrix of the models on an infinite line were elucidated; here, we consider finite-size behaviour. TBA equations are proposed for all cases related to phi(21) and phi(12) perturbations of unitary minimal models. These are subjected to a variety of checks in the ultraviolet and infrared limits, and compared with results from a recently-proposed nonlinear integral equation. A nonlinear integral equation is also used to study the flows from tricritical to critical models, over the full range of q. Our results should also be of relevance to the study of the off-critical dilute A models in regimes 1 and 2.