{
  "id": "1108.1034",
  "version": "v2",
  "published": "2011-08-04T09:48:29.000Z",
  "updated": "2011-11-02T10:58:10.000Z",
  "title": "The Sherrington-Kirkpatrick model near T_c and near T=0",
  "authors": [
    "A. Crisanti",
    "C. De Dominicis"
  ],
  "comment": "11 pages, 3 figures, Published version",
  "journal": "Philosophical Magazine 2011, 1-12, iFirst",
  "doi": "10.1080/14786435.2011.611120",
  "categories": [
    "cond-mat.dis-nn",
    "cond-mat.stat-mech"
  ],
  "abstract": "Some recent results concerning the Sherrington-Kirkpatrick model are reported. For $T$ near the critical temperature $T_c$, the replica free energy of the Sherrington-Kirkpatrick model is taken as the starting point of an expansion in powers of $\\delta Q_{ab} = (Q_{ab} - Q_{ab}^{\\rm RS})$ about the Replica Symmetric solution $Q_{ab}^{\\rm RS}$. The expansion is kept up to 4-th order in $\\delta{\\bm Q}$ where a Parisi solution $Q_{ab} = Q(x)$ emerges, but only if one remains close enough to $T_c$. For $T$ near zero we show how to separate contributions from $x\\ll T\\ll 1$ where the Hessian maintains the standard structure of Parisi Replica Symmetry Breaking with bands of eigenvalues bounded below by zero modes. For $T\\ll x \\leq 1$ the bands collapse and only two eigenvalues, a null one and a positive one, are found. In this region the solution stands in what can be called a {\\sl droplet-like} regime.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2011-11-02T10:58:10.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "sherrington-kirkpatrick model",
      "replica free energy",
      "replica symmetric solution",
      "solution stands",
      "eigenvalues"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "journal": "Philosophical Magazine",
      "year": 2012,
      "month": "Jan",
      "volume": 92,
      "number": "1-3",
      "pages": 280
    },
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 922208,
      "adsabs": "2012PMag...92..280C"
    }
  }
}