Unified criteria for crystallization in hard-core lattice systems with applications to polyomino fluids and multi-component mixtures
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arXiv
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866918365583376384 |
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| author | He, Qidong |
| author_facet | He, Qidong |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_05294 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Unified criteria for crystallization in hard-core lattice systems with applications to polyomino fluids and multi-component mixtures He, Qidong Mathematical Physics Statistical Mechanics Probability 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. |
| title | Unified criteria for crystallization in hard-core lattice systems with applications to polyomino fluids and multi-component mixtures |
| topic | Mathematical Physics Statistical Mechanics Probability |
| url | https://arxiv.org/abs/2602.05294 |