{
  "id": "2004.05337",
  "version": "v1",
  "published": "2020-04-11T08:31:29.000Z",
  "updated": "2020-04-11T08:31:29.000Z",
  "title": "On delocalization in the six-vertex model",
  "authors": [
    "Marcin Lis"
  ],
  "comment": "24 pages",
  "categories": [
    "math.PR",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We show that the six-vertex model with parameter $c\\in[\\sqrt 3, 2]$ on a square lattice torus has an ergodic infinite-volume limit as the size of the torus grows to infinity. Moreover we prove that for $c\\in[\\sqrt{2+\\sqrt 2}, 2]$, the associated height function on $\\mathbb Z^2$ has unbounded variance. The proof relies on an extension of the Baxter-Kelland-Wu representation of the six-vertex model to multi-point correlation functions of the associated spin model. Other crucial ingredients are the uniqueness and percolation properties of the critical random cluster measure for $q\\in[1,4]$, and recent results relating the decay of correlations in the spin model with the delocalization of the height function.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-04-11T08:31:29.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "82B20",
      "60K35"
    ],
    "keywords": [
      "six-vertex model",
      "delocalization",
      "height function",
      "square lattice torus",
      "ergodic infinite-volume limit"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}