{
  "id": "1710.05411",
  "version": "v1",
  "published": "2017-10-15T22:16:04.000Z",
  "updated": "2017-10-15T22:16:04.000Z",
  "title": "A continuum of pure states in the Ising model on a halfplane",
  "authors": [
    "Douglas Abraham",
    "Charles M. Newman",
    "Senya Shlosman"
  ],
  "comment": "2 figures",
  "categories": [
    "math-ph",
    "cond-mat.stat-mech",
    "math.MP"
  ],
  "abstract": "We study the homogeneous nearest-neighbor Ising ferromagnet on the right half plane with a Dobrushin type boundary condition --- say plus on the top part of the boundary and minus on the bottom. For sufficiently low temperature $T$, we completely characterize the pure (i.e., extremal) Gibbs states, as follows. There is exactly one for each angle $\\theta\\in\\lbrack-\\pi/2,+\\pi/2]$; here $\\theta$ specifies the asymptotic angle of the interface separating regions where the spin configuration looks like that of the plus (respectively, minus) full-plane state. Some of these conclusions are extended all the way to $T=T_{c}$ by developing new Ising exact solution result -- in particular, there is at least one pure state for each $\\theta$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-10-15T22:16:04.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "82B20"
    ],
    "keywords": [
      "pure state",
      "ising model",
      "dobrushin type boundary condition",
      "right half plane",
      "spin configuration looks"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}