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

2026/07/26 by Lewis Bowen, Marcus Michelen, Will Perkins
#math-ph #math.DS #math.MP #math.PR

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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 ℝ² and ℝ³ 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.

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• A Percolating Hard Sphere Model