{
  "id": "cond-mat/0302538",
  "version": "v2",
  "published": "2003-02-26T10:44:57.000Z",
  "updated": "2003-04-10T10:30:46.000Z",
  "title": "On the Parisi-Toulouse hypothesis for the spin glass phase in mean-field theory",
  "authors": [
    "A. Crisanti",
    "T. Rizzo",
    "T. Temesvari"
  ],
  "comment": "6 pages, 2 figures",
  "journal": "Eur. Phys. J. B 33, 203-207 (2003)",
  "doi": "10.1140/epjb/e2003-00157-8",
  "categories": [
    "cond-mat.dis-nn",
    "cond-mat.stat-mech"
  ],
  "abstract": "We consider the spin-glass phase of the Sherrington-Kirkpatrick model in the presence of a magnetic field. The series expansion of the Parisi function $q(x)$ is computed at high orders in powers of $\\tau=T_c-T$ and $H$. We find that none of the Parisi-Toulouse scaling hypotheses on the $q(x)$ behavior strictly holds, although some of them are violated only at high orders. The series is resummed yielding results in the whole spin-glass phase which are compared with those from a numerical evaluation of the $q(x)$. At the high order considered, the transition turns out to be third order on the Almeida-Thouless line, a result which is confirmed rigorously computing the expansion of the solution near the line at finite $\\tau$. The transition becomes smoother for infinitesimally small field while it is third order at strictly zero field.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2003-04-10T10:30:46.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "spin glass phase",
      "mean-field theory",
      "parisi-toulouse hypothesis",
      "high order",
      "spin-glass phase"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 6,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}