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| Format: | Preprint |
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2025
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| Accès en ligne: | https://arxiv.org/abs/2512.10142 |
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| _version_ | 1866909956494589952 |
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| author | Park, S. C. |
| author_facet | Park, S. C. |
| contents | We show on non-flat but critical s-embeddings the celebrated convergence of the interface curves of the critical FK Ising model to an $\operatorname{SLE}_{16/3}$ curve, using discrete complex analytic techniques first used in arXiv:0708.0039, arXiv:1312.0533 and subsequently extended to more lattice settings including isoradial graphs arXiv:0910.2045, circle packings arXiv:1712.08736, and flat s-embeddings arXiv:2006.14559. In our setting, the s-embedding approximates a maximal surface in the Minkowski space $\mathbb R^{2,1}$, an `exact' criticality condition identified in arXiv:2006.14559, which is stronger than the percolation-theoretic `near-critical' setup studied in, e.g., arXiv:2309.08470. The proof relies on a careful discretisation of the Laplace-Beltrami operator on the s-embedding, which is crucial in identifying the limit of the martingale observable. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_10142 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Conformal Invariance of the FK-Ising Model on Lorentz-Maximal S-Embeddings Park, S. C. Probability Mathematical Physics We show on non-flat but critical s-embeddings the celebrated convergence of the interface curves of the critical FK Ising model to an $\operatorname{SLE}_{16/3}$ curve, using discrete complex analytic techniques first used in arXiv:0708.0039, arXiv:1312.0533 and subsequently extended to more lattice settings including isoradial graphs arXiv:0910.2045, circle packings arXiv:1712.08736, and flat s-embeddings arXiv:2006.14559. In our setting, the s-embedding approximates a maximal surface in the Minkowski space $\mathbb R^{2,1}$, an `exact' criticality condition identified in arXiv:2006.14559, which is stronger than the percolation-theoretic `near-critical' setup studied in, e.g., arXiv:2309.08470. The proof relies on a careful discretisation of the Laplace-Beltrami operator on the s-embedding, which is crucial in identifying the limit of the martingale observable. |
| title | Conformal Invariance of the FK-Ising Model on Lorentz-Maximal S-Embeddings |
| topic | Probability Mathematical Physics |
| url | https://arxiv.org/abs/2512.10142 |