{
  "id": "0712.0790",
  "version": "v2",
  "published": "2007-12-05T18:15:27.000Z",
  "updated": "2007-12-10T22:25:20.000Z",
  "title": "Glauber dynamics for the mean-field Ising model: cut-off, critical power law, and metastability",
  "authors": [
    "David A. Levin",
    "Malwina J. Luczak",
    "Yuval Peres"
  ],
  "comment": "40 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "We study the Glauber dynamics for the Ising model on the complete graph, also known as the Curie-Weiss Model. For beta < 1, we prove that the dynamics exhibits a cut-off: the distance to stationarity drops from near 1 to near 0 in a window of order n centered at [2(1-beta)]^{-1} n log n. For beta = 1, we prove that the mixing time is of order n^{3/2}. For beta > 1, we study metastability. In particular, we show that the Glauber dynamics restricted to states of non-negative magnetization has mixing time O(n log n).",
  "revisions": [
    {
      "version": "v2",
      "updated": "2007-12-10T22:25:20.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60J10",
      "60K35",
      "82C20"
    ],
    "keywords": [
      "glauber dynamics",
      "mean-field ising model",
      "critical power law",
      "complete graph",
      "curie-weiss model"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 40,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0712.0790L"
    }
  }
}