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arXiv · 2607.23873

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

Lewis Bowen·Marcus Michelen·Will Perkins
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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 $\mathbb{R}^2$ 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.

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Lewis Bowen, Marcus Michelen, Will Perkins. 2026-07-26. A phase transition for the hard sphere model on the hyperbolic plane. https://arxiv.org/abs/2607.23873

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