{
  "id": "cond-mat/0606425",
  "version": "v2",
  "published": "2006-06-15T17:09:13.000Z",
  "updated": "2006-11-21T08:16:28.000Z",
  "title": "On Equilibrium Dynamics of Spin-Glass Systems",
  "authors": [
    "A. Crisanti",
    "L. Leuzzi"
  ],
  "comment": "24 pages, 6 figures",
  "journal": "Phys. Rev. B 75, 144301 (2007)",
  "doi": "10.1103/PhysRevB.75.144301",
  "categories": [
    "cond-mat.dis-nn",
    "cond-mat.stat-mech"
  ],
  "abstract": "We present a critical analysis of the Sompolinsky theory of equilibrium dynamics. By using the spherical $2+p$ spin glass model we test the asymptotic static limit of the Sompolinsky solution showing that it fails to yield a thermodynamically stable solution. We then present an alternative formulation, based on the Crisanti, H\\\"orner and Sommers [Z. f\\\"ur Physik {\\bf 92}, 257 (1993)] dynamical solution of the spherical $p$-spin spin glass model, reproducing a stable static limit that coincides, in the case of a one step Replica Symmetry Breaking Ansatz, with the solution at the dynamic free energy threshold at which the relaxing system gets stuck off-equilibrium. We formally extend our analysis to any number of Replica Symmetry Breakings $R$. In the limit $R\\to\\infty$ both formulations lead to the Parisi anti-parabolic differential equation. This is the special case, though, where no dynamic blocking threshold occurs. The new formulation does not contain the additional order parameter $\\Delta$ of the Sompolinsky theory.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2006-11-21T08:16:28.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "equilibrium dynamics",
      "spin-glass systems",
      "dynamic free energy threshold",
      "parisi anti-parabolic differential equation",
      "static limit"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "APS",
      "journal": "Phys. Rev. B"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}