The Wulff crystal of self-dual FK-percolation becomes round when approaching criticality
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866918393518489600 |
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| author | Manolescu, Ioan Mohanarangan, Maran |
| author_facet | Manolescu, Ioan Mohanarangan, Maran |
| contents | The study of the phase transition in planar FK-percolation on the square lattice has seen significant recent breakthroughs. The model undergoes a change in the nature of its phase transition at $q = 4$, transitioning from a continuous to a discontinuous regime. The aim of this article is to investigate the behaviour of the model in the discontinuous regime as $q > 4$ approaches the continuous transition point $4$ from above, while maintaining the critical parameter $p = p_c(q)$. We prove that in this limit, the correlation length becomes isotropic. The core of the proof builds upon the recently established rotational invariance of the large-scale features of the model at $q = 4$ (arXiv:2012.11672). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_16318 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The Wulff crystal of self-dual FK-percolation becomes round when approaching criticality Manolescu, Ioan Mohanarangan, Maran Probability Mathematical Physics 60K35 (Primary) 82B43, 82B27 (Secondary) The study of the phase transition in planar FK-percolation on the square lattice has seen significant recent breakthroughs. The model undergoes a change in the nature of its phase transition at $q = 4$, transitioning from a continuous to a discontinuous regime. The aim of this article is to investigate the behaviour of the model in the discontinuous regime as $q > 4$ approaches the continuous transition point $4$ from above, while maintaining the critical parameter $p = p_c(q)$. We prove that in this limit, the correlation length becomes isotropic. The core of the proof builds upon the recently established rotational invariance of the large-scale features of the model at $q = 4$ (arXiv:2012.11672). |
| title | The Wulff crystal of self-dual FK-percolation becomes round when approaching criticality |
| topic | Probability Mathematical Physics 60K35 (Primary) 82B43, 82B27 (Secondary) |
| url | https://arxiv.org/abs/2603.16318 |