{
  "id": "2012.13750",
  "version": "v1",
  "published": "2020-12-26T14:37:52.000Z",
  "updated": "2020-12-26T14:37:52.000Z",
  "title": "Delocalization of the height function of the six-vertex model",
  "authors": [
    "Hugo Duminil-Copin",
    "Alex Karrila",
    "Ioan Manolescu",
    "Mendes Oulamara"
  ],
  "comment": "54 pages, 16 figures",
  "categories": [
    "math.PR",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We show that the height function of the six-vertex model, in the parameter range $\\mathbf a=\\mathbf b=1$ and $\\mathbf c\\ge1$, is delocalized with logarithmic variance when $\\mathbf c\\le 2$. This complements the earlier proven localization for $\\mathbf c>2$. Our proof relies on Russo--Seymour--Welsh type arguments, and on the local behaviour of the free energy of the cylindrical six-vertex model, as a function of the unbalance between the number of up and down arrows.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-12-26T14:37:52.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60K35",
      "82B20",
      "82B27"
    ],
    "keywords": [
      "height function",
      "delocalization",
      "earlier proven localization",
      "russo-seymour-welsh type arguments",
      "logarithmic variance"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 54,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}