Equation of state and isothermal compressibility for the hard hexagon model in the disordered regime

The equation of state for the hard hexagon model in the disordered regime is computed. The isothermal compressibility is given as a rational function of K and p. The hard hexagon model is a lattice gas on a triangular lattice with the rule that if a site is occupied, then the six neighbouring sites are necessarily vacant. Baxter (1980, 1981) has shown that this model is exactly solvable by the method of commuting transfer matrices (Baxter 1972, 1982). In the disordered regime, Baxter's exact results are