{
  "id": "0811.1524",
  "version": "v2",
  "published": "2008-11-10T17:19:51.000Z",
  "updated": "2009-04-07T11:27:24.000Z",
  "title": "Phase diagram and large deviations in the free-energy of mean-field spin-glasses",
  "authors": [
    "Giorgio Parisi",
    "Tommaso Rizzo"
  ],
  "comment": "Detailed study of the phase diagram and proof of the fifth order scaling at all temperatures, final version accepted on PRB",
  "journal": "Phys. Rev. B 79, 134205 (2009)",
  "doi": "10.1103/PhysRevB.79.134205",
  "categories": [
    "cond-mat.dis-nn",
    "cond-mat.stat-mech"
  ],
  "abstract": "We consider the probability distribution of large deviations in the spin-glass free energy for the Sherrington-Kirkpatrick mean field model, i.e. the exponentially small probability of finding a system with intensive free energy smaller than the most likely one. This result is obtained by computing $\\Phi(n,T)=T \\bar{Z^n}/ n$, i.e. the average value of the partition function to the power $n$ as a function of $n$. We study in full details the phase diagram of $\\Phi(n,T)$ in the $(n,T)$ plane computing in particular the stability of the replica-symmetric solution. At low temperatures we compute $\\Phi(n,T)$ in series of $n$ and $\\tau=T_c-T$ at high orders using the standard hierarchical ansatz and confirm earlier findings on the $O(n^5)$ scaling. We prove that the $O(n^5)$ scaling is valid at all orders and obtain an exact expression for the coefficient in term of the function $q(x)$. Resumming the series we obtain the large deviations probability at all temperatures. At zero temperature the analytical prediction displays a remarkable quantitative agreement with the numerical data. A similar computation for the simpler spherical model is also performed and the connection between large and small deviations is discussed.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2009-04-07T11:27:24.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "75.50.Lk"
    ],
    "keywords": [
      "phase diagram",
      "mean-field spin-glasses",
      "sherrington-kirkpatrick mean field model",
      "free-energy",
      "spin-glass free energy"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "APS",
      "journal": "Physical Review B",
      "year": 2009,
      "month": "Apr",
      "volume": 79,
      "number": 13,
      "pages": 134205
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009PhRvB..79m4205P"
    }
  }
}