Universality of Ising spin correlations on critical doubly-periodic graphs
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866911242378018816 |
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| author | Mahfouf, Rémy |
| author_facet | Mahfouf, Rémy |
| contents | We establish conformal invariance of Ising spin correlations on critical doubly periodic graphs, showing that their scaling limit coincides with that of the critical square lattice, as originally proved by Chelkak, Hongler and Izyurov. To overcome the absence of integrability and quantitative full plane constructions in the periodic setting, we combine discrete analytic tools with random cluster methods. This result completes the universality picture for periodic lattices, whose criticality condition was identified by Cimasoni and Duminil-Copin and whose conformal structure and interface convergence were obtained by Chelkak. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_25019 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Universality of Ising spin correlations on critical doubly-periodic graphs Mahfouf, Rémy Probability Mathematical Physics 82B20 We establish conformal invariance of Ising spin correlations on critical doubly periodic graphs, showing that their scaling limit coincides with that of the critical square lattice, as originally proved by Chelkak, Hongler and Izyurov. To overcome the absence of integrability and quantitative full plane constructions in the periodic setting, we combine discrete analytic tools with random cluster methods. This result completes the universality picture for periodic lattices, whose criticality condition was identified by Cimasoni and Duminil-Copin and whose conformal structure and interface convergence were obtained by Chelkak. |
| title | Universality of Ising spin correlations on critical doubly-periodic graphs |
| topic | Probability Mathematical Physics 82B20 |
| url | https://arxiv.org/abs/2510.25019 |