Scaling limit of domino tilings on a pentagonal domain
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Acceso en línea: | |
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| _version_ | 1866929609921003520 |
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| author | Colomo, Filippo Pronko, Andrei G. |
| author_facet | Colomo, Filippo Pronko, Andrei G. |
| contents | We consider the six-vertex model at its free-fermion point with domain wall boundary conditions, which is equivalent to random domino tilings of the Aztec diamond. We compute the scaling limit of a particular non-local correlation function, essentially equivalent to the partition function for the domino tilings of a pentagon-shaped domain, obtained by cutting away a triangular region from a corner of the initial Aztec diamond. We observe a third-order phase transition when the geometric parameters of the obtained pentagonal domain are tuned to have the fifth side exactly tangent to the arctic ellipse of the corresponding initial model. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_07849 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Scaling limit of domino tilings on a pentagonal domain Colomo, Filippo Pronko, Andrei G. Mathematical Physics Statistical Mechanics Probability We consider the six-vertex model at its free-fermion point with domain wall boundary conditions, which is equivalent to random domino tilings of the Aztec diamond. We compute the scaling limit of a particular non-local correlation function, essentially equivalent to the partition function for the domino tilings of a pentagon-shaped domain, obtained by cutting away a triangular region from a corner of the initial Aztec diamond. We observe a third-order phase transition when the geometric parameters of the obtained pentagonal domain are tuned to have the fifth side exactly tangent to the arctic ellipse of the corresponding initial model. |
| title | Scaling limit of domino tilings on a pentagonal domain |
| topic | Mathematical Physics Statistical Mechanics Probability |
| url | https://arxiv.org/abs/2407.07849 |