{
  "id": "1505.06716",
  "version": "v1",
  "published": "2015-05-25T18:57:06.000Z",
  "updated": "2015-05-25T18:57:06.000Z",
  "title": "Large cycles in random permutations related to the Heisenberg model",
  "authors": [
    "J. E. Björnberg"
  ],
  "comment": "11 pages",
  "categories": [
    "math.PR",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We study the weighted version of the interchange process where a permutation receives weight $\\theta^{\\#\\mathrm{cycles}}$. For $\\theta=2$ this is T\\'oth's representation of the quantum Heisenberg ferromagnet on the complete graph. We prove, for $\\theta>1$, that large cycles appear at `low temperature'.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-05-25T18:57:06.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "random permutations",
      "heisenberg model",
      "permutation receives weight",
      "quantum heisenberg ferromagnet",
      "large cycles appear"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}