Scaling Limit of RSOS Models and TBA Equations

TL;DR

This paper derives TBA equations for off-critical RSOS models, revealing massive and massless scattering regimes and their relation to conformal field theories, focusing on the ground state in specific regimes.

Contribution

It systematically derives TBA equations from elliptic functional equations for RSOS models, focusing on the ground state in regimes III and IV, and clarifies their physical interpretations.

Findings

TBA equations are massive in Regime III.

TBA equations are massless in Regime IV.

Flow between different conformal field theories is described.

Abstract

We study the scaling limits of the L-state Restricted Solid-on-Solid (RSOS) lattice models and their fusion hierarchies in the off-critical regimes. Starting with the elliptic functional equations of Klumper and Pearce, we derive the Thermodynamic Bethe Ansatz (TBA) equations of Zamolodchikov. Although this systematic approach, in principle, allows TBA equations to be derived for all the excited states we restrict our attention here to the largest eigenvalue or groundstate in Regimes III and IV. In Regime III the TBA equations are massive while in Regime IV there is massless scattering describing the renormalization group flow between distinct A_1^{(1)} coset conformal field theories. Regimes I and II, pertaining to Z_{L-1} parafermions, will be treated in a subsequent paper.