{
  "id": "1005.0954",
  "version": "v2",
  "published": "2010-05-06T09:50:42.000Z",
  "updated": "2010-09-17T12:59:13.000Z",
  "title": "Low-temperature dynamics of the Curie-Weiss Model: Periodic orbits, multiple histories, and loss of Gibbsianness",
  "authors": [
    "Victor Ermolaev",
    "Christof Kuelske"
  ],
  "comment": "31 pages, 24 figures",
  "categories": [
    "math-ph",
    "math.MP",
    "math.PR"
  ],
  "abstract": "We consider the Curie-Weiss model at a given initial temperature in vanishing external field evolving under a Glauber spin-flip dynamics corresponding to a possibly different temperature. We study the limiting conditional probabilities and their continuity properties and discuss their set of points of discontinuity (bad points). We provide a complete analysis of the transition between Gibbsian and non-Gibbsian behavior as a function of time, extending earlier work for the case of independent spin-flip dynamics. For initial temperature bigger than one we prove that the time-evolved measure stays Gibbs forever, for any (possibly low) temperature of the dynamics. In the regime of heating to low-temperatures from even lower temperatures, when the initial temperature is smaller than the temperature of the dynamics, and smaller than 1, we prove that the time-evolved measure is Gibbs initially and becomes non-Gibbs after a sharp transition time. We find this regime is further divided into a region where only symmetric bad configurations exist, and a region where this symmetry is broken. In the regime of further cooling from low-temperatures there is always symmetry-breaking in the set of bad configurations. These bad configurations are created by a new mechanism which is related to the occurrence of periodic orbits for the vector field which describes the dynamics of Euler-Lagrange equations for the path large deviation functional for the order parameter. To our knowledge this is the first example of the rigorous study of non-Gibbsian phenomena related to cooling, albeit in a mean-field setup.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2010-09-17T12:59:13.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "82C26",
      "82C05",
      "82B26"
    ],
    "keywords": [
      "curie-weiss model",
      "periodic orbits",
      "low-temperature dynamics",
      "multiple histories",
      "initial temperature"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "doi": "10.1007/s10955-010-0074-x",
      "journal": "Journal of Statistical Physics",
      "year": 2010,
      "month": "Dec",
      "volume": 141,
      "number": 5,
      "pages": 727
    },
    "note": {
      "typesetting": "TeX",
      "pages": 31,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010JSP...141..727E"
    }
  }
}