{
  "id": "2104.07629",
  "version": "v1",
  "published": "2021-04-15T17:46:57.000Z",
  "updated": "2021-04-15T17:46:57.000Z",
  "title": "Spin glass to paramagnetic transition in Spherical Sherrington-Kirkpatrick model with ferromagnetic interaction",
  "authors": [
    "Iain M. Johnstone",
    "Yegor Klochkov",
    "Alexei Onatski",
    "Damian Pavlyshyn"
  ],
  "comment": "31 pages, 3 figures",
  "categories": [
    "math.PR"
  ],
  "abstract": "This paper studies fluctuations of the free energy of the Spherical Sherrington-Kirkpatrick model with ferromagnetic Curie-Weiss interaction with coupling constant $J \\in [0,1)$ and inverse temperature $\\beta$. We consider the critical temperature regime $\\beta=1+bN^{-1/3}\\sqrt{\\log N}$, $b\\in\\mathbb{R}$. For $b \\leq 0$, the limiting distribution of the free energy is Gaussian. As $b$ increases from $0$ to $\\infty$, we describe the transition of the limiting distribution from Gaussian to Tracy-Widom.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-04-15T17:46:57.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60F05",
      "60B20"
    ],
    "keywords": [
      "spherical sherrington-kirkpatrick model",
      "spin glass",
      "paramagnetic transition",
      "ferromagnetic interaction",
      "free energy"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 31,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}