Algorithms for the computation of polynomial relationships for the hard hexagon model

Abstract

We calculate the polynomial relationships P( ϱ, z) = 0 and P( ϱ, κ) = 0 in both the ordered and disordered regimes for the hard hexagon model. We start with Baxter's exact solution which gives the physical quantities κ, ϱ, and z parametrically as a function of a variable τ and exploit the modular properties of Baxter's solution. Using elementary Riemann surface theory, the computation can be reduced to algorithms involving only linear algebra. These algorithms are implemented using a computer algebra system. The method will be applicable to other exactly solvable models in which cusp expansions can be computed.