{
  "id": "1306.6207",
  "version": "v3",
  "published": "2013-06-26T11:37:26.000Z",
  "updated": "2014-05-30T14:58:37.000Z",
  "title": "Third-order phase transition in random tilings",
  "authors": [
    "F. Colomo",
    "A. G. Pronko"
  ],
  "comment": "21 pages, 6 figures; v3: journal version with misprints in text and Fig. 3 corrected; footnote added at page 3",
  "journal": "Phys. Rev. E 88 (2013), 042125 (11 pp.)",
  "doi": "10.1103/PhysRevE.88.042125",
  "categories": [
    "math-ph",
    "cond-mat.stat-mech",
    "hep-th",
    "math.CO",
    "math.MP"
  ],
  "abstract": "We consider the domino tilings of an Aztec diamond with a cut-off corner of macroscopic square shape and given size, and address the bulk properties of tilings as the size is varied. We observe that the free energy exhibits a third-order phase transition when the cut-off square, increasing in size, reaches the arctic ellipse---the phase separation curve of the original (unmodified) Aztec diamond. We obtain this result by studying the thermodynamic limit of certain nonlocal correlation function of the underlying six-vertex model with domain wall boundary conditions, the so-called emptiness formation probability (EFP). We consider EFP in two different representations: as a tau-function for Toda chains and as a random matrix model integral. The latter has a discrete measure and a linear potential with hard walls; the observed phase transition shares properties with both Gross-Witten-Wadia and Douglas-Kazakov phase transitions.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2014-05-30T14:58:37.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05.20.-y",
      "05.50.+q",
      "63.10.+a"
    ],
    "keywords": [
      "third-order phase transition",
      "random tilings",
      "arctic ellipse-the phase separation curve",
      "aztec diamond",
      "domain wall boundary conditions"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "APS",
      "journal": "Physical Review E",
      "year": 2013,
      "month": "Oct",
      "volume": 88,
      "number": 4,
      "pages": "042125"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 1240121,
      "adsabs": "2013PhRvE..88d2125C"
    }
  }
}