{
  "id": "0712.4091",
  "version": "v2",
  "published": "2007-12-26T00:54:24.000Z",
  "updated": "2008-01-03T22:54:19.000Z",
  "title": "Exact solution of the six-vertex model with domain wall boundary conditions. Ferroelectric phase",
  "authors": [
    "Pavel Bleher",
    "Karl Liechty"
  ],
  "comment": "22 pages, 7 figures",
  "categories": [
    "math-ph",
    "math.MP"
  ],
  "abstract": "This is a continuation of the paper [4] of Bleher and Fokin, in which the large $n$ asymptotics is obtained for the partition function $Z_n$ of the six-vertex model with domain wall boundary conditions in the disordered phase. In the present paper we obtain the large $n$ asymptotics of $Z_n$ in the ferroelectric phase. We prove that for any $\\ep>0$, as $n\\to\\infty$, $Z_n=CG^nF^{n^2}[1+O(e^{-n^{1-\\ep}})]$, and we find the exact value of the constants $C,G$ and $F$. The proof is based on the large $n$ asymptotics for the underlying discrete orthogonal polynomials and on the Toda equation for the tau-function.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2008-01-03T22:54:19.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "82B23"
    ],
    "keywords": [
      "domain wall boundary conditions",
      "six-vertex model",
      "ferroelectric phase",
      "exact solution",
      "underlying discrete orthogonal polynomials"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0712.4091B"
    }
  }
}