Solvable lattice models labelled by Dynkin diagrams

TL;DR

This paper establishes a connection between RSOS models and loop models, classifies solvable RSOS models using Dynkin diagrams, and introduces an off-critical extension that breaks certain symmetries.

Contribution

It introduces a new classification of solvable RSOS models via Dynkin diagrams and extends one model off-criticality, breaking Z2 symmetry.

Findings

Established equivalence between RSOS and loop models

Classified solvable RSOS models by Dynkin diagrams

Developed off-critical extension breaking Z2 symmetry

Abstract

An equivalence between generalised restricted solid-on-solid (RSOS) models, associated with sets of graphs, and multi-colour loop models is established. As an application we consider solvable loop models and in this way obtain new solvable families of critical RSOS models. These families can all be classified by the Dynkin diagrams of the simply-laced Lie algebras. For one of the RSOS models, labelled by the Lie algebra pair (A$_L$,A$_L$) and related to the C$_2^{(1)}$ vertex model, we give an off-critical extension, which breaks the Z$_2$ symmetry of the Dynkin diagrams.