{
  "id": "1406.1206",
  "version": "v1",
  "published": "2014-06-04T20:40:51.000Z",
  "updated": "2014-06-04T20:40:51.000Z",
  "title": "On the probability of staying above a wall for the (2+1)-dimensional SOS model at low temperature",
  "authors": [
    "Pietro Caputo",
    "Fabio Martinelli",
    "Fabio Lucio Toninelli"
  ],
  "comment": "19 pages, 6 figures",
  "categories": [
    "math.PR",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We obtain sharp asymptotics for the probability that the (2+1)-dimensional discrete SOS interface at low temperature is positive in a large region. For a square region $\\Lambda$, both under the infinite volume measure and under the measure with zero boundary conditions around $\\Lambda$, this probability turns out to behave like $\\exp(-\\tau_\\beta(0) L \\log L )$, with $\\tau_\\beta(0)$ the surface tension at zero tilt, also called step free energy, and $L$ the box side. This behavior is qualitatively different from the one found for continuous height massless gradient interface models.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-06-04T20:40:51.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60K35",
      "60F10",
      "82B41",
      "82C24"
    ],
    "keywords": [
      "low temperature",
      "sos model",
      "probability",
      "height massless gradient interface models",
      "infinite volume measure"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1406.1206C"
    }
  }
}