{
  "id": "1106.3118",
  "version": "v4",
  "published": "2011-06-15T23:14:02.000Z",
  "updated": "2013-08-12T11:47:46.000Z",
  "title": "Selection of measure and a Large Deviation Principle for the general XY model",
  "authors": [
    "Artur O. Lopes",
    "Jairo Mengue"
  ],
  "categories": [
    "math.DS",
    "cond-mat.stat-mech",
    "math-ph",
    "math.MP",
    "math.PR"
  ],
  "abstract": "We consider $(M,d)$ a connected and compact manifold and we denote by $X$ the Bernoulli space $M^{\\mathbb{N}}$. The shift acting on $X$ is denoted by $\\sigma$. We analyze the general XY model, as presented in a recent paper by A. T. Baraviera, L. M. Cioletti, A. O. Lopes, J. Mohr and R. R. Souza. Denote the Gibbs measure by $\\mu_{c}:=h_{c}\\nu_{c}$, where $h_{c}$ is the eigenfunction, and, $\\nu_{c}$ is the eigenmeasure of the Ruelle operator associated to $cf$. We are going to prove that any measure selected by $\\mu_{c}$, as $c\\to +\\infty$, is a maximizing measure for $f$. We also show, when the maximizing probability measure is unique, that it is true a Large Deviation Principle, with the deviation function $R_{+}^{\\infty}=\\sum_{j=0}^\\infty R_{+} (\\sigma^f)$, where $R_{+}:= \\beta(f) + V\\circ\\sigma - V - f$, and, $V$ is any calibrated subaction.",
  "revisions": [
    {
      "version": "v4",
      "updated": "2013-08-12T11:47:46.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37A60",
      "37A50",
      "37A05",
      "82B05"
    ],
    "keywords": [
      "large deviation principle",
      "general xy model",
      "bernoulli space",
      "compact manifold",
      "gibbs measure"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1106.3118L"
    }
  }
}