{
  "id": "0803.3918",
  "version": "v2",
  "published": "2008-03-27T14:15:16.000Z",
  "updated": "2008-04-29T07:57:35.000Z",
  "title": "Universality class of replica symmetry breaking, scaling behavior, and the low-temperature fixed-point order function of the Sherrington-Kirkpatrick model",
  "authors": [
    "Reinhold Oppermann",
    "Manuel J. Schmidt"
  ],
  "doi": "10.1103/PhysRevE.78.061124",
  "categories": [
    "cond-mat.dis-nn"
  ],
  "abstract": "A scaling theory of replica symmetry breaking (RSB) in the SK-model is presented in the framework of critical phenomena for the scaling regime of small inverse RSB-orders, small temperatures, small magnetic fields, and near opposite pseudo-dynamic limits. We employ the pseudo-dynamical picture (PRL98, 127201 (2007)) with two critical points, where separated temperature- and magnetic field-scaling is obtained. An unconventional scaling hypothesis for the free energy is given, modeling this separated scaling in accordance with detailed numerical self-consistent solutions for up to 200 orders of RSB. A divergent correlation-length describes the RSB-criticality as a long-range correlation effect occurring on the pseudo-lattice of RSB-orders. Rational-valued exponents are concluded with high precision from high-order RSB scaling and by using a new fixed point extrapolation method. Power laws, scaling relations, and scaling functions are analyzed.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2008-04-29T07:57:35.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "75.10.Nr",
      "75.40.-s",
      "89.75.Da"
    ],
    "keywords": [
      "low-temperature fixed-point order function",
      "replica symmetry breaking",
      "sherrington-kirkpatrick model",
      "universality class",
      "scaling behavior"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "APS",
      "journal": "Physical Review E",
      "year": 2008,
      "month": "Dec",
      "volume": 78,
      "number": 6,
      "pages": "061124"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008PhRvE..78f1124O"
    }
  }
}