Baxter Hard Hexagon Model

Hard Hexagon Model (Baxter 1980): Particles occupy sites of a triangular lattice; no two adjacent sites may be simultaneously occupied (hard-core exclusion with hexagonal footprint). This model has an exact solution via the Yang-Baxter equation.

Phase transition: At critical fugacity z_c = ((√5+1)/2)⁵ ≈ 11.09, the system undergoes a continuous phase transition in the universality class of the 3-state Potts model (central charge c=4/5). Below z_c: disordered (fluid). Above z_c: one of three ordered sublattices dominates.

Exact density: ρ(z) is given by Rogers-Ramanujan functions — one of the most celebrated exact results in statistical mechanics.