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

Forrester, P.J.; Baxter, R.J.

doi:10.1007/BF01010471

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

1985

38 pages

Published in:

J.Statist.Phys. 38 (1985) 3-4, 435-472

DOI:

10.1007/BF01010471

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Abstract: (Springer)

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 heightl i restricted to the range 1⩽l i ⩽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.

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