Massive and massless phases in self-dual $Z_N$ spin models: some exact results from the thermodynamic Bethe ansatz

TL;DR

This paper investigates the phase diagrams of two-dimensional $Z_N$ spin models, proposing integral equations to describe RG flows and analyzing their infrared behavior in both massless and massive phases.

Contribution

It introduces integral equations to model phase transitions and RG flows in $Z_N$ spin models, providing exact results and detailed analysis of their infrared behavior.

Findings

Proposed integral equations describe RG flows in $Z_N$ models.

Analyzed infrared behavior in massless and massive phases.

Applied techniques to other models.

Abstract

The generally accepted phase diagrams for the discrete $Z_N$ spin models in two dimensions imply the existence of certain renormalisation group flows, both between conformal field theories and into a massive phase. Integral equations are proposed to describe these flows, and some properties of their solutions are discussed. The infrared behaviour in massless and massive directions is analysed in detail, and the techniques used are applied to a number of other models.