The hard hexagon, RSOS and chiral Potts models

Abstract

Abstract This chapter presents the exact results for the grand partition function of the hard hexagon model in both low and high density regions are presented. In the low density region, these results are used to derive the first 25 virial coefficients of the virial expansion. The analyticity of the pressure in the density plane in both the low and high density regions are then presented. The general theory of the chiral Potts model as a two-dimensional statistical model is presented and the eigenvalues of the three-component superintegrable case are computed in detail. The order parameter is discussed and the phase diagram of the general three-component integrable chiral Potts spin chain is given. Open questions are discussed about Q operators, eight-vertex model degeneracies, and conjectures for correlations functions of the superintegrable chiral Potts model.