Further exact solutions of the eight-vertex SOS model and generalizations of the Rogers-Ramanujan identities

Abstract

The restricted eight-vertex solid-on-solid (SOS) model is an exactly solvable class of two-dimensional lattice models. To each site i of the lattice there is associated an integer height li restricted to the range 1≤li≤r-1. The Boltzmann weights of the model are expressed in terms of elliptic functions of period 2 K, and involve a parameter η. In an earlier paper we considered the case η=K/r. Here we generalize those considerations to the case η=sK/r, s an integer relatively prime to r. We are again led to generalizations of the Rogers-Ramanujan identities. © 1985 Plenum Publishing Corporation.