A phase transition for the hard sphere model on the hyperbolic plane

Abstract

The hard sphere model is a classical model from statistical physics in which particles are represented by equal-sized spheres. Longstanding predictions from the physics literature indicate that in ${\mathbb{R}}^2$ and ${\mathbb{R}}^3$ the system undergoes a phase transition, but it remains a major open problem to confirm this. We prove the existence of a phase transition for this model in the hyperbolic plane.

42 pages, 5 figures