{
  "id": "2004.13272",
  "version": "v1",
  "published": "2020-04-28T03:56:16.000Z",
  "updated": "2020-04-28T03:56:16.000Z",
  "title": "Nonexistence and Uniqueness for Pure States of Ferroelectric Six-Vertex Models",
  "authors": [
    "Amol Aggarwal"
  ],
  "comment": "35 pages, no figures",
  "categories": [
    "math.PR",
    "math-ph",
    "math.MP"
  ],
  "abstract": "In this paper we consider the existence and uniqueness of pure states with some fixed slope $(s, t) \\in [0, 1]^2$ for a general ferroelectric six-vertex model. First, we show there is an open subset $\\mathfrak{H} \\subset [0, 1]^2$, which is parameterized by the region between two explicit hyperbolas, such that there is no pure state for the ferroelectric six-vertex model of any slope $(s, t) \\in \\mathfrak{H}$. Second, we show that there is a unique pure state for this model of any slope $(s, t)$ on the boundary $\\partial \\mathfrak{H}$ of $\\mathfrak{H}$. These results confirm predictions of Bukman-Shore from 1995.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-04-28T03:56:16.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "uniqueness",
      "nonexistence",
      "general ferroelectric six-vertex model",
      "unique pure state",
      "results confirm predictions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 35,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}