We improve upon all known lower bounds on the critical fugacity and critical density of the hard sphere model in dimensions two and higher. As the dimension tends to infinity our improvements are by factors of $2$ and $1.7$, respectively. We make these improvements by utilizing techniques from theoretical computer science to show that a certain Markov chain for sampling from the hard sphere model mixes rapidly at low enough fugacities. We then prove an equivalence between optimal spatial and temporal mixing for hard spheres, an equivalence that is well-known for a wide class of discrete spin systems.

中文翻译：

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通过马尔可夫链对硬球进行相关衰减

我们改进了硬球模型在二维和更高维度上的临界逸度和临界密度的所有已知下限。由于维度趋于无穷大，我们的改进分别是 2 美元和 1.7 美元。我们通过利用理论计算机科学的技术来进行这些改进，以表明用于从硬球模型采样的某个马尔可夫链在足够低的逸度下快速混合。然后，我们证明了硬球最佳空间和时间混合之间的等价性，这种等价性对于广泛的离散自旋系统是众所周知的。