High-fugacity expansion and crystallization in non-sliding hard-core lattice particle models without a tiling constraint
Fuente:
arXiv
Guardado en:
| Autores principales: | , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2024
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866909716886585344 |
|---|---|
| author | He, Qidong Jauslin, Ian |
| author_facet | He, Qidong Jauslin, Ian |
| contents | In this paper, we prove the existence of a crystallization transition for a family of hard-core particle models on periodic graphs in arbitrary dimensions. We establish a criterion under which crystallization occurs at sufficiently high densities. The criterion is more general than that in [Jauslin, Lebowitz, Comm. Math. Phys. 364:2, 2018], as it allows models in which particles do not tile the space in the close-packing configurations, such as discrete hard-disk models. To prove crystallization, we prove that the pressure is analytic in the inverse of the fugacity for large enough complex fugacities, using Pirogov-Sinai theory. One of the main tools used for this result is the definition of a local density, based on a discrete generalization of Voronoi cells. We illustrate the criterion by proving that it applies to two examples: staircase models and the radius 2.5 hard-disk model on the square lattice. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_02615 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | High-fugacity expansion and crystallization in non-sliding hard-core lattice particle models without a tiling constraint He, Qidong Jauslin, Ian Mathematical Physics Statistical Mechanics Probability In this paper, we prove the existence of a crystallization transition for a family of hard-core particle models on periodic graphs in arbitrary dimensions. We establish a criterion under which crystallization occurs at sufficiently high densities. The criterion is more general than that in [Jauslin, Lebowitz, Comm. Math. Phys. 364:2, 2018], as it allows models in which particles do not tile the space in the close-packing configurations, such as discrete hard-disk models. To prove crystallization, we prove that the pressure is analytic in the inverse of the fugacity for large enough complex fugacities, using Pirogov-Sinai theory. One of the main tools used for this result is the definition of a local density, based on a discrete generalization of Voronoi cells. We illustrate the criterion by proving that it applies to two examples: staircase models and the radius 2.5 hard-disk model on the square lattice. |
| title | High-fugacity expansion and crystallization in non-sliding hard-core lattice particle models without a tiling constraint |
| topic | Mathematical Physics Statistical Mechanics Probability |
| url | https://arxiv.org/abs/2402.02615 |