{
  "id": "0904.3088",
  "version": "v2",
  "published": "2009-04-20T19:27:04.000Z",
  "updated": "2009-12-16T18:55:00.000Z",
  "title": "Exact solution of the six-vertex model with domain wall boundary conditions. Antiferroelectric phase",
  "authors": [
    "Pavel Bleher",
    "Karl Liechty"
  ],
  "comment": "69 pages, 10 figures",
  "doi": "10.1007/s00220-008-0709-9",
  "categories": [
    "math-ph",
    "math.MP"
  ],
  "abstract": "We obtain the large $n$ asymptotics of the partition function $Z_n$ of the six-vertex model with domain wall boundary conditions in the antiferroelectric phase region, with the weights $a=\\sinh(\\ga-t), b=\\sinh(\\ga+t), c=\\sinh(2\\ga), |t|<\\ga$. We prove the conjecture of Zinn-Justin, that as $n\\to\\infty$, $Z_n=C\\th_4(n\\om) F^{n^2}[1+O(n^{-1})]$, where $\\om$ and $F$ are given by explicit expressions in $\\ga$ and $t$, and $\\th_4(z)$ is the Jacobi theta function. The proof is based on the Riemann-Hilbert approach to the large $n$ asymptotic expansion of the underlying discrete orthogonal polynomials and on the Deift-Zhou nonlinear steepest descent method.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2009-12-16T18:55:00.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "domain wall boundary conditions",
      "six-vertex model",
      "antiferroelectric phase",
      "exact solution",
      "deift-zhou nonlinear steepest descent method"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "Springer",
      "journal": "Communications in Mathematical Physics",
      "year": 2009,
      "month": "Mar",
      "volume": 286,
      "number": 2,
      "pages": 777
    },
    "note": {
      "typesetting": "TeX",
      "pages": 69,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009CMaPh.286..777B"
    }
  }
}