{
  "id": "2502.08394",
  "version": "v1",
  "published": "2025-02-12T13:36:47.000Z",
  "updated": "2025-02-12T13:36:47.000Z",
  "title": "Exploring the phase transition of planar FK-percolation",
  "authors": [
    "Ioan Manolescu"
  ],
  "comment": "Lecture notes for a mini-course given at the 2023 CIME summer school \"Statistical Mechanics and Stochastic PDEs''",
  "categories": [
    "math.PR"
  ],
  "abstract": "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.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2025-02-12T13:36:47.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60K35",
      "82B43",
      "82B27"
    ],
    "keywords": [
      "phase transition",
      "planar fk-percolation",
      "favour quick access",
      "important results valid",
      "asymptotic rotational invariance"
    ],
    "tags": [
      "lecture notes"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}