{
  "id": "math/0409046",
  "version": "v1",
  "published": "2004-09-03T09:41:16.000Z",
  "updated": "2004-09-03T09:41:16.000Z",
  "title": "An Analysis of Ising Type Models On Cayley Tree by a Contour Argument",
  "authors": [
    "U. A. Rozikov"
  ],
  "comment": "17 pages",
  "categories": [
    "math.PR",
    "math-ph",
    "math.MP"
  ],
  "abstract": "In the paper the Ising model with competing $J_1$ and $J_2$ interactions with spin values $\\pm 1$, on a Cayley tree of order 2 (with 3 neighbors) is considered . We study the structure of the ground states and verify the Peierls condition for the model. Our second result gives description of Gibbs measures for ferromagnetic Ising model with $J_1<0$ and $J_2=0$, using a contour argument which we also develop in the paper. By the argument we also study Gibbs measures for a natural generalization of the Ising model. We discuss some open problems and state several conjectures.\\",
  "revisions": [
    {
      "version": "v1",
      "updated": "2004-09-03T09:41:16.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60K35",
      "82B05",
      "82B20"
    ],
    "keywords": [
      "ising type models",
      "cayley tree",
      "contour argument",
      "study gibbs measures",
      "natural generalization"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004math......9046R"
    }
  }
}