{
  "id": "1512.04441",
  "version": "v1",
  "published": "2015-12-14T18:18:44.000Z",
  "updated": "2015-12-14T18:18:44.000Z",
  "title": "Free energy in the mixed p-spin models with vector spins",
  "authors": [
    "Dmitry Panchenko"
  ],
  "categories": [
    "math.PR",
    "math-ph",
    "math.MP"
  ],
  "abstract": "Using the synchronization mechanism developed in the previous work on the Potts spin glass model, arXiv:1512.00370, we obtain the analogue of the Parisi formula for the free energy in the mixed even $p$-spin models with vector spins, which include the Sherrington-Kirkpatrick model with vector spins interacting through their scalar product. As a special case, this also establishes the sharpness of Talagrand's upper bound for the free energy of multiple mixed $p$-spin systems coupled by constraining their overlaps.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-12-14T18:18:44.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60F10",
      "60G15",
      "60K35",
      "82B44"
    ],
    "keywords": [
      "free energy",
      "vector spins",
      "mixed p-spin models",
      "potts spin glass model",
      "talagrands upper bound"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv151204441P"
    }
  }
}