Exploring the phase transition of planar FK-percolation
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866909519498444800 |
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| author | Manolescu, Ioan |
| author_facet | Manolescu, Ioan |
| contents | The aim of these notes is to give a quick introduction to FK-percolation, focusing on certain recent results about the phase transition of the two dimensional model, namely its continuity or discontinuity depending on the cluster weight $q$, and the asymptotic rotational invariance of the critical phase (when the phase transition is continuous). As such, the main focus is on FK-percolation on $\mathbb Z^2$ with $q \geq 1$, but we do mention some important results valid for general dimension. To favour quick access to recent results, the style is minimal, with certain proofs omitted or left as exercises. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_08394 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Exploring the phase transition of planar FK-percolation Manolescu, Ioan Probability 60K35, 82B43, 82B27 The aim of these notes is to give a quick introduction to FK-percolation, focusing on certain recent results about the phase transition of the two dimensional model, namely its continuity or discontinuity depending on the cluster weight $q$, and the asymptotic rotational invariance of the critical phase (when the phase transition is continuous). As such, the main focus is on FK-percolation on $\mathbb Z^2$ with $q \geq 1$, but we do mention some important results valid for general dimension. To favour quick access to recent results, the style is minimal, with certain proofs omitted or left as exercises. |
| title | Exploring the phase transition of planar FK-percolation |
| topic | Probability 60K35, 82B43, 82B27 |
| url | https://arxiv.org/abs/2502.08394 |