{
  "id": "0910.4091",
  "version": "v2",
  "published": "2009-10-21T13:48:47.000Z",
  "updated": "2010-01-18T09:16:05.000Z",
  "title": "Sherrington-Kirkpatrick model near $T=T_c$: expanding around the Replica Symmetric Solution",
  "authors": [
    "A. Crisanti",
    "C. De Dominicis"
  ],
  "comment": "18 pages, 3 figures",
  "journal": "J. Phys. A: Math. Theor. 43 (2010) 055002",
  "doi": "10.1088/1751-8113/43/5/055002",
  "categories": [
    "cond-mat.dis-nn",
    "cond-mat.stat-mech"
  ],
  "abstract": "An expansion for the free energy functional of the Sherrington-Kirkpatrick (SK) model, around the Replica Symmetric SK solution $Q^{({\\rm RS})}_{ab} = \\delta_{ab} + q(1-\\delta_{ab})$ is investigated. In particular, when the expansion is truncated to fourth order in. $Q_{ab} - Q^{({\\rm RS})}_{ab}$. The Full Replica Symmetry Broken (FRSB) solution is explicitly found but it turns out to exist only in the range of temperature $0.549...\\leq T\\leq T_c=1$, not including T=0. On the other hand an expansion around the paramagnetic solution $Q^{({\\rm PM})}_{ab} = \\delta_{ab}$ up to fourth order yields a FRSB solution that exists in a limited temperature range $0.915...\\leq T \\leq T_c=1$.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2010-01-18T09:16:05.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "replica symmetric solution",
      "sherrington-kirkpatrick model",
      "full replica symmetry broken",
      "replica symmetric sk solution",
      "fourth order yields"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "journal": "Journal of Physics A Mathematical General",
      "year": 2010,
      "month": "Feb",
      "volume": 43,
      "number": 5,
      "pages": "055002"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010JPhA...43e5002C"
    }
  }
}