{
  "id": "1406.4702",
  "version": "v2",
  "published": "2014-06-18T13:00:56.000Z",
  "updated": "2015-02-25T00:01:16.000Z",
  "title": "Structure of finite-RSB asymptotic Gibbs measures in the diluted spin glass models",
  "authors": [
    "Dmitry Panchenko"
  ],
  "categories": [
    "math.PR",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We suggest a possible approach to proving the M\\'ezard-Parisi formula for the free energy in the diluted spin glass models, such as diluted K-spin or random K-sat model at any positive temperature. In the main contribution of the paper, we show that a certain small modification of the Hamiltonian in any of these models forces all finite-RSB asymptotic Gibbs measures in the sense of the overlaps to satisfy the M\\'ezard-Parisi ansatz for the distribution of spins. Unfortunately, what is still missing is a description of the general full-RSB asymptotic Gibbs measures. If one could show that the general case can be approximated by finite-RSB case in the right sense then one could a posteriori remove the small modification of the Hamiltonian to recover the M\\'ezard-Parisi formula for the original model.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-06-18T13:00:56.000Z",
      "comment": null,
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2015-02-25T00:01:16.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60K35",
      "60G09",
      "82B44"
    ],
    "keywords": [
      "finite-rsb asymptotic gibbs measures",
      "diluted spin glass models",
      "general full-rsb asymptotic gibbs measures",
      "small modification"
    ],
    "publication": {
      "doi": "10.1007/s10955-015-1385-8",
      "journal": "Journal of Statistical Physics",
      "year": 2016,
      "month": "Jan",
      "volume": 162,
      "number": 1,
      "pages": 1
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2016JSP...162....1P"
    }
  }
}