Exact results for the adsorption of a dense fluid onto a triangular lattice of sticky sites

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Abstract
A discussion of exact results for the interface between a dense fluid of molecules with a spherical hard core of diameter σ and a triangular lattice of sticky sites with spacing d on a wall with hard repulsive potential is given. When σ≤d and first neighbors attract, there is a first order transition when the stickiness parameter λ, singlet wall density ρ01(0), and pair correlation function g02(d) satisfy λρ01(0)[g02(d)]3=1. If d<σ< 7/8 d, and further neighbors do not interact, the model is equivalent to the hard hexagon model solved by Baxter. In this case there is a second order phase transition between an ordered 7/8 × 7/8 phase and a disordered one.