{
  "id": "1510.03414",
  "version": "v1",
  "published": "2015-10-12T19:57:51.000Z",
  "updated": "2015-10-12T19:57:51.000Z",
  "title": "The Legendre structure of the Parisi formula",
  "authors": [
    "Antonio Auffinger",
    "Wei-Kuo Chen"
  ],
  "comment": "20 pages",
  "categories": [
    "math.PR",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We show that the Parisi formula of the mixed $p$-spin model is a concave function of the squared inverse temperature. This allows us to derive a new expression for the Parisi formula that involves the inverse temperature and the functional order parameter as Legendre conjugate variables.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-10-12T19:57:51.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60K35",
      "82B44"
    ],
    "keywords": [
      "parisi formula",
      "legendre structure",
      "legendre conjugate variables",
      "functional order parameter",
      "concave function"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv151003414A"
    }
  }
}