Journal article

8-VERTEX SOS MODEL AND GENERALIZED ROGERS-RAMANUJAN-TYPE IDENTITIES

GE ANDREWS, RJ BAXTER, PJ FORRESTER

Journal of Statistical Physics | PLENUM PUBL CORP | Published : 1984

Abstract

The eight-vertex model is equivalent to a "solid-on-solid" (SOS) model, in which an integer height li is associated with each site i of the square lattice. The Boltzmann weights of the model are expressed in terms of elliptic functions of period 2 K, and involve a variable parameter η. Here we begin by showing that the hard hexagon model is a special case of this eight-vertex SOS model, in which η=K/5 and the heights are restricted to the range 1≤li≤4. We remark that the calculation of the sublattice densities of the hard hexagon model involves the Rogers-Ramanujan and related identities. We then go on to consider a more general eight-vertex SOS model, with η=K/r (r an integer) and 1≤li≤r-1...

View full abstract

University of Melbourne Researchers