{
  "id": "1109.0449",
  "version": "v1",
  "published": "2011-09-02T14:06:07.000Z",
  "updated": "2011-09-02T14:06:07.000Z",
  "title": "Metastability in the dilute Ising model",
  "authors": [
    "T. Bodineau",
    "B. Graham",
    "M. Wouts"
  ],
  "comment": "49 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "Consider Glauber dynamics for the Ising model on the hypercubic lattice with a positive magnetic field. Starting from the minus configuration, the system initially settles into a metastable state with negative magnetization. Slowly the system relaxes to a stable state with positive magnetization. Schonmann and Shlosman showed that in the two dimensional case the relaxation time is a simple function of the energy required to create a critical Wulff droplet. The dilute Ising model is obtained from the regular Ising model by deleting a fraction of the edges of the underlying graph. In this paper we show that even an arbitrarily small dilution can dramatically reduce the relaxation time. This is because of a catalyst effect---rare regions of high dilution speed up the transition from minus phase to plus phase.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-09-02T14:06:07.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60K35",
      "82C41"
    ],
    "keywords": [
      "dilute ising model",
      "relaxation time",
      "metastability",
      "catalyst effect-rare regions",
      "glauber dynamics"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 49,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1109.0449B"
    }
  }
}