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

The restricted eight-vertex solid-on-solid (SOS) model is an exactly solvable class of two-dimensional lattice models. To each sitei of the lattice there is associated an integer heightli restricted to the range 1⩽li⩽r−1. The Boltzmann weights of the model are expressed in terms of elliptic functions of period 2K, and involve a parameterη. In an earlier paper we considered the caseη=K/r. Here we generalize those considerations to the caseη=sK/r, s an integer relatively prime tor. We are again led to generalizations of the Rogers-Ramanujan identities.