Relations between Potts and RSOS models on a torus

TL;DR

This paper establishes exact identities linking the partition functions of Q-state Potts models and RSOS models on a torus, revealing deep connections between these models across all temperatures and sizes.

Contribution

It introduces exact identities between modified partition functions of Potts and RSOS models on a torus, valid at any temperature and size, with a discussion on their field theoretic interpretation.

Findings

Exact identities between partition functions of the models

Validity of identities for any temperature and finite size

Discussion of the field theoretic interpretation

Abstract

We study the relationship between Q-state Potts models and staggered RSOS models of the A\_{p-1} type on a torus, with sqrt(Q)=2 cos(pi / p). In general the partition functions of these models differ due to clusters of non-trivial topology. However we find exact identities, valid for any temperature and any finite size of the torus, between various modified partition functions in the two pictures. The field theoretic interpretation of these modified partition function is discussed.