Deviations from critical density in the generalised hard hexagon model

Abstract

Ramanujan's elliptic function identities and others are used to obtain infinite product forms for the deviations rho - rho c from the critical density rho c=1/2(1-5-12/) in the four regimes of the generalised hard hexagon model. Product forms are also obtained for the singular part rho sing of the density confirming the simple scaling forms recently conjectured by Huse, (1983).