{
  "id": "1505.07349",
  "version": "v1",
  "published": "2015-05-27T14:40:31.000Z",
  "updated": "2015-05-27T14:40:31.000Z",
  "title": "Fluctuations of the free energy of the spherical Sherrington-Kirkpatrick model",
  "authors": [
    "Jinho Baik",
    "Ji Oon Lee"
  ],
  "comment": "40 pages",
  "categories": [
    "math.PR",
    "math-ph",
    "math.MP"
  ],
  "abstract": "The spherical Sherrington-Kirkpatrick model is a spherical mean field model for spin glass. We consider the fluctuations of the free energy at arbitrary non-critical temperature for the 2-spin model with no magnetic field. We show that in the high temperature regime the law of the fluctuations converges to the Gaussian distribution just like in the Sherrington-Kirtkpatrick model. We show, on the other hand, that the law of the fluctuations is given by the GOE Tracy-Widom distribution in the low temperature regime. The orders of the fluctuations are markedly different in these two regimes. A universality of the limit law is also proved.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-05-27T14:40:31.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "spherical sherrington-kirkpatrick model",
      "free energy",
      "fluctuations",
      "goe tracy-widom distribution",
      "high temperature regime"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 40,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150507349B"
    }
  }
}