{
  "id": "1902.04909",
  "version": "v1",
  "published": "2019-02-13T14:10:56.000Z",
  "updated": "2019-02-13T14:10:56.000Z",
  "title": "Gradient Gibbs measures for the SOS model with countable values on a Cayley tree",
  "authors": [
    "F. Henning",
    "C. Kuelske",
    "A. Le Ny",
    "U. A. Rozikov"
  ],
  "comment": "24 pages, 3 figures",
  "categories": [
    "math.PR"
  ],
  "abstract": "We consider an SOS (solid-on-solid) model, with spin values from the set of all integers, on a Cayley tree of order k and are interested in translation-invariant gradient Gibbs measures (GGMs) of the model. Such a measure corresponds to a boundary law (a function defined on vertices of the Cayley tree) satisfying a functional equation. In the ferromagnetic SOS case on the binary tree we find up to five solutions to a class of 4-periodic boundary law equations (in particular, some 2-periodic ones). We show that these boundary laws define up to four distinct GGMs. Moreover, we construct some 3-periodic boundary laws on the Cayley tree of arbitrary order k, which define GGMs different from the 4-periodic ones.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-02-13T14:10:56.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "82B26",
      "60K35"
    ],
    "keywords": [
      "cayley tree",
      "sos model",
      "countable values",
      "translation-invariant gradient gibbs measures",
      "boundary laws define"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}