{
  "id": "math-ph/0609046",
  "version": "v1",
  "published": "2006-09-16T10:17:31.000Z",
  "updated": "2006-09-16T10:17:31.000Z",
  "title": "Uniqueness of Gibbs states of a quantum system on graphs",
  "authors": [
    "D. Kepa",
    "Y. Kozitsky"
  ],
  "comment": "9 pages",
  "doi": "10.1016/S0034-4877(07)80064-4",
  "categories": [
    "math-ph",
    "math.MP"
  ],
  "abstract": "Gibbs states of an infinite system of interacting quantum particles are considered. Each particle moves on a compact Riemannian manifold and is attached to a vertex of a graph (one particle per vertex). Two kinds of graphs are studied: (a) a general graph with locally finite degree; (b) a graph with globally bounded degree. In case (a), the uniqueness of Gibbs states is shown under the condition that the interaction potentials are uniformly bounded by a sufficiently small constant. In case (b), the interaction potentials are random. In this case, under a certain condition imposed on the probability distribution of these potentials the almost sure uniqueness of Gibbs states has been shown.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2006-09-16T10:17:31.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "82B10"
    ],
    "keywords": [
      "gibbs states",
      "quantum system",
      "uniqueness",
      "interaction potentials",
      "compact riemannian manifold"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}