Limit shapes for Domain-Wall (colored) vertex models
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866911184113893376 |
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| author | Di Francesco, Philippe Keating, David |
| author_facet | Di Francesco, Philippe Keating, David |
| contents | We study partition functions with domain-wall like boundary conditions for path models issued from colored vertex models. These models display an arctic phenomenon, as attested by numerical simulations. We show that the colored vertex model is equivalent to a certain single-color ``colorblind" vertex model. In a special case of the weights for the colorblind touching paths, we derive the arctic curve using a bijective sliding map to non-intersecting paths, for which arctic curves were previously derived using the tangent method. The resulting arctic curves are only piecewise analytic, as in the known non-free fermion cases of Six vertex model with domain-wall boundaries and its relatives. We also prove a shear phenomenon, that some portions of the arctic curve are sheared versions of the analytic continuation of other portions, as already observed in the uniformly weighted Six and Twenty vertex models. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_25442 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Limit shapes for Domain-Wall (colored) vertex models Di Francesco, Philippe Keating, David Mathematical Physics Statistical Mechanics Combinatorics We study partition functions with domain-wall like boundary conditions for path models issued from colored vertex models. These models display an arctic phenomenon, as attested by numerical simulations. We show that the colored vertex model is equivalent to a certain single-color ``colorblind" vertex model. In a special case of the weights for the colorblind touching paths, we derive the arctic curve using a bijective sliding map to non-intersecting paths, for which arctic curves were previously derived using the tangent method. The resulting arctic curves are only piecewise analytic, as in the known non-free fermion cases of Six vertex model with domain-wall boundaries and its relatives. We also prove a shear phenomenon, that some portions of the arctic curve are sheared versions of the analytic continuation of other portions, as already observed in the uniformly weighted Six and Twenty vertex models. |
| title | Limit shapes for Domain-Wall (colored) vertex models |
| topic | Mathematical Physics Statistical Mechanics Combinatorics |
| url | https://arxiv.org/abs/2509.25442 |