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arXiv · 2602.05294

Unified criteria for crystallization in hard-core lattice systems with applications to polyomino fluids and multi-component mixtures

Qidong He
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Abstract

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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Qidong He. 2026-02-05. Unified criteria for crystallization in hard-core lattice systems with applications to polyomino fluids and multi-component mixtures. https://arxiv.org/abs/2602.05294

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