{
  "id": "0712.2658",
  "version": "v1",
  "published": "2007-12-17T09:15:41.000Z",
  "updated": "2007-12-17T09:15:41.000Z",
  "title": "Dynamics of an Ising Spin Glass on the Bethe Lattice",
  "authors": [
    "Martin Kiemes",
    "Heinz Horner"
  ],
  "comment": "18 pages, contribution for the special issue \"Viewing the World through Spin Glasses\" in honour of Professor David Sherrington",
  "doi": "10.1088/1751-8113/41/32/324017",
  "categories": [
    "cond-mat.dis-nn"
  ],
  "abstract": "We study the dynamical low temperature behaviour of the Ising spin glass on the Bethe lattice. Starting from Glauber dynamics we propose a cavity like Ansatz that allows for the treatment of the slow (low temperature) part of dynamics. Assuming a continuous phase transitions and ultrametricity with respect to long time scales we approach the problem perturbatively near the critical temperature. The theory is formulated in terms of correlation-response-functions of arbitrary order. They can, however, be broken down completely to products of pair functions depending on two time arguments only. For binary couplings $J=\\pm I$ a spin glass solution is found which approaches the corresponding solution for the SK-model in the limit of high connectivity. For more general distributions $P(J)$ no stable or marginal solution of this type appears to exist. The nature of the low temperature phase in this more general case is unclear.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2007-12-17T09:15:41.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "ising spin glass",
      "bethe lattice",
      "low temperature phase",
      "dynamical low temperature behaviour",
      "long time scales"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "journal": "Journal of Physics A Mathematical General",
      "year": 2008,
      "month": "Aug",
      "volume": 41,
      "number": 32,
      "pages": 324017
    },
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008JPhA...41F4017K"
    }
  }
}