{
  "id": "cond-mat/0103375",
  "version": "v1",
  "published": "2001-03-19T05:34:26.000Z",
  "updated": "2001-03-19T05:34:26.000Z",
  "title": "Against Chaos in Temperature in Mean-Field Spin-Glass Models",
  "authors": [
    "Tommaso Rizzo"
  ],
  "comment": "20 pages, submitted to J.Phys. A",
  "journal": "J. Phys. A: Math. Gen. 34 (2001) 5531-5549",
  "doi": "10.1088/0305-4470/34/27/305",
  "categories": [
    "cond-mat.dis-nn"
  ],
  "abstract": "We study the problem of chaos in temperature in some mean-field spin-glass models by means of a replica computation over a model of coupled systems. We propose a set of solutions of the saddle point equations which are intrinsically non-chaotic and solve a general problem regarding the consistency of their structure. These solutions are relevant in the case of uncoupled systems too, therefore they imply a non-trivial overlap distribution $P(q_{T1T2})$ between systems at different temperatures. The existence of such solutions is checked to fifth order in an expansion near the critical temperature through highly non-trivial cancellations, while it is proved that a dangerous set of such cancellations holds exactly at all orders in the Sherrington-Kirkpatrick (SK) model. The SK model with soft-spin distribution is also considered obtaining analogous results. Previous analytical results are discussed.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2001-03-19T05:34:26.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "mean-field spin-glass models",
      "temperature",
      "saddle point equations",
      "non-trivial overlap distribution",
      "general problem"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "journal": "Journal of Physics A Mathematical General",
      "year": 2001,
      "month": "Jul",
      "volume": 34,
      "number": 27,
      "pages": 5531
    },
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2001JPhA...34.5531R"
    }
  }
}