{
  "id": "1207.3580",
  "version": "v1",
  "published": "2012-07-16T05:28:10.000Z",
  "updated": "2012-07-16T05:28:10.000Z",
  "title": "The shape of the $(2+1)$D SOS surface above a wall",
  "authors": [
    "Pietro Caputo",
    "Eyal Lubetzky",
    "Fabio Martinelli",
    "Allan Sly",
    "Fabio Lucio Toninelli"
  ],
  "comment": "5 pages",
  "journal": "Comptes Rendus Mathematique 350(13-14):703-706, 2012",
  "categories": [
    "math.PR",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We give a full description for the shape of the classical (2+1)\\Dim Solid-On-Solid model above a wall, introduced by Temperley (1952). On an $L\\times L$ box at a large inverse-temperature $\\beta$ the height of most sites concentrates on a single level $h = \\lfloor (1/4\\beta)\\log L\\rfloor$ for most values of $L$. For a sequence of diverging boxes the ensemble of level lines of heights $(h,h-1,...)$ has a scaling limit in Hausdorff distance iff the fractional parts of $(1/4\\beta)\\log L$ converge to a noncritical value. The scaling limit is explicitly given by nested distinct loops formed via translates of Wulff shapes. Finally, the $h$-level lines feature $L^{1/3+o(1)}$ fluctuations from the side boundaries.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-07-16T05:28:10.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60K35",
      "82C22"
    ],
    "keywords": [
      "sos surface",
      "scaling limit",
      "level lines feature",
      "hausdorff distance",
      "solid-on-solid model"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 5,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1207.3580C"
    }
  }
}