{
  "id": "1903.01030",
  "version": "v1",
  "published": "2019-03-04T01:15:57.000Z",
  "updated": "2019-03-04T01:15:57.000Z",
  "title": "The generalized TAP free energy II",
  "authors": [
    "Wei-Kuo Chen",
    "Dmitry Panchenko",
    "Eliran Subag"
  ],
  "comment": "28 pages",
  "categories": [
    "math.PR",
    "math-ph",
    "math.MP"
  ],
  "abstract": "In a recent paper [14], we developed the generalized TAP approach for mixed $p$-spin models with Ising spins at positive temperature. Here we extend these results in two directions. We find a simplified representation for the energy of the generalized TAP states in terms of the Parisi measure of the model and, in particular, show that the energy of all states at a given distance from the origin is the same. Furthermore, we prove the analogues of the positive temperature results at zero temperature, which concern the ground-state energy and the organization of ground-state configurations in space.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-03-04T01:15:57.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60F10",
      "60G15",
      "60K35",
      "82B44"
    ],
    "keywords": [
      "generalized tap free energy",
      "parisi measure",
      "spin models",
      "generalized tap approach",
      "generalized tap states"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 28,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}