Automorphic properties of local height probabilities for integrable solid-on-solid models

Abstract

The local height probabilities of a class of integrable solid-on-solid models are obtained in terms of the modular forms describing irreducible decompositions of tensor products of $A_1^{\mathrm{}\left(1\right)\mathrm{}}$ modules. Their critical exponents agree with those of a coset construction of Goddard-Kent-Olive with c not necessarily less than 1.