{
  "id": "1111.0144",
  "version": "v4",
  "published": "2011-11-01T08:41:16.000Z",
  "updated": "2014-02-13T22:48:01.000Z",
  "title": "The near-critical planar FK-Ising model",
  "authors": [
    "Hugo Duminil-Copin",
    "Christophe Garban",
    "Gábor Pete"
  ],
  "comment": "34 pages, 8 figures. This is a streamlined version; the previous one contains more explanations and additional material on exceptional times in FK models with general $q$. Furthermore, the statement and proof of Theorem 1.2 have slightly changed",
  "journal": "Comm. Math. Phys. 326 (2014), no. 1, 1--35",
  "categories": [
    "math.PR",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We study the near-critical FK-Ising model. First, a determination of the correlation length defined via crossing probabilities is provided. Second, a phenomenon about the near-critical behavior of FK-Ising is highlighted, which is completely missing from the case of standard percolation: in any monotone coupling of FK configurations $\\omega_p$ (e.g., in the one introduced in [Gri95]), as one raises $p$ near $p_c$, the new edges arrive in a self-organized way, so that the correlation length is not governed anymore by the number of pivotal edges at criticality.",
  "revisions": [
    {
      "version": "v4",
      "updated": "2014-02-13T22:48:01.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "near-critical planar fk-ising model",
      "correlation length",
      "standard percolation",
      "fk configurations",
      "pivotal edges"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "Springer",
      "journal": "Communications in Mathematical Physics",
      "doi": "10.1007/s00220-013-1857-0",
      "year": 2014,
      "month": "Feb",
      "volume": 326,
      "number": 1,
      "pages": 1
    },
    "note": {
      "typesetting": "TeX",
      "pages": 34,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014CMaPh.326....1D"
    }
  }
}