{
  "id": "1707.07626",
  "version": "v1",
  "published": "2017-07-24T16:05:16.000Z",
  "updated": "2017-07-24T16:05:16.000Z",
  "title": "About the slab percolation threshold for the Potts model in dimension $d\\ge4$",
  "authors": [
    "Hugo Duminil-Copin",
    "Vincent Tassion"
  ],
  "comment": "7 pages",
  "categories": [
    "math.PR",
    "math-ph",
    "math.MP"
  ],
  "abstract": "The object of this short note is to show that the critical inverse temperature of the Potts model on $\\mathbb Z^3\\times[-k,k]^{d-3}$ converges to the critical inverse temperature of the model on $\\mathbb Z^d$. As an application, we prove that the probability that $0$ is connected to distance $n$ but not to infinity is decaying exponentially fast for the supercritical random-cluster model on $\\mathbb Z^d$ ($d\\ge4$) associated to the Potts model. We briefly mention the connection between the present result and the classical problem of proving that the so-called slab percolation threshold coincides with the critical value for Potts models.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-07-24T16:05:16.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "potts model",
      "critical inverse temperature",
      "slab percolation threshold coincides",
      "supercritical random-cluster model",
      "short note"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 7,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}