AI 中文总结
研究双曲平面上硬球模型的相变问题，通过证明得出该模型在双曲平面存在相变，解决了物理学文献中长期未证实的相关预测问题。
AI 中文摘要
硬球模型是统计物理中的经典模型，粒子由等大球体表示。长期以来物理学文献预测在\(\mathbb{R}^2\)和\(\mathbb{R}^3\)中该系统会发生相变，但尚未证实。本文证明了该模型在双曲平面上存在相变。
英文摘要
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.
Comments42 pages, 5 figures
