{
  "id": "math/0405359",
  "version": "v1",
  "published": "2004-05-18T22:12:54.000Z",
  "updated": "2004-05-18T22:12:54.000Z",
  "title": "A note on the free energy of the coupled system in the Sherrington-Kirkpatrick model",
  "authors": [
    "Dmitry Panchenko"
  ],
  "comment": "16 pages",
  "journal": "2005 Markov Process. Related Fields 11 No. 1",
  "categories": [
    "math.PR",
    "cond-mat.dis-nn"
  ],
  "abstract": "In this paper we consider a system of spins that consists of two configurations $\\vsi^1,\\vsi^2\\in\\Sigma_N=\\{-1,+1\\}^N$ with Gaussian Hamiltonians $H_N^1(\\vsi^1)$ and $H_N^2(\\vsi^2)$ correspondingly, and these configurations are coupled on the set where their overlap is fixed $\\{R_{1,2}=N^{-1}\\sum_{i=1}^N \\sigma_i^1\\sigma_i^2 = u_N\\}.$ We prove the existence of the thermodynamic limit of the free energy of this system given that $\\lim_{N\\to\\infty}u_N = u\\in[-1,1]$ and give the analogue of the Aizenman-Sims-Starr variational principle that describes this limit via random overlap structures.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2004-05-18T22:12:54.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60K35",
      "82B44"
    ],
    "keywords": [
      "free energy",
      "sherrington-kirkpatrick model",
      "coupled system",
      "aizenman-sims-starr variational principle",
      "random overlap structures"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004math......5359P"
    }
  }
}