硬核晶格系统中结晶统一标准的提出及其在多边形流体和多组分混合物中的应用
Unified criteria for crystallization in hard-core lattice systems with applications to polyomino fluids and multi-component mixtures
AI总结：
本文提出了一种统一的结晶标准，适用于硬核晶格系统中的多边形流体和多组分混合物，通过体积分配规则和Pirogov-Sinai理论的扩展进行证明。
摘要：
我们提出了两个先前由Jauslin、Lebowitz和作者开发的高逸度结晶标准的统一扩展。我们的新标准以存在具有 desirable 优化和筛选性质的体积分配规则来表述，类似于Hales证明开普勒猜想时构造的评分函数。值得注意的是，我们的结果适用于具有离散旋转自由度的大量多边形模型及其手性混合物，以及具有多种几何上不同的粒子形状的多组分混合物。证明使用了Mazel-Stuhl-Suhov对具有无限相互作用的系统进行的最新系统扩展的Pirogov-Sinai理论。
英文摘要：
We present a unified extension of two sets of criteria for high-fugacity crystallization in hard-core lattice systems developed previously by Jauslin, Lebowitz, and the author. Our new criterion is formulated in terms of the existence of a volume allocation rule with desirable optimization and screening properties, in analogy to the scoring function constructed in Hales' proof of the Kepler conjecture. Notably, our result applies to a large class of polyomino models with discrete rotational degrees of freedom and their chiral mixtures, as well as multi-component mixtures featuring several geometrically distinct particle shapes. The proof uses a recent systematic extension of Pirogov--Sinai theory to systems with infinite interactions by Mazel--Stuhl--Suhov.
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