{
  "id": "1610.03941",
  "version": "v1",
  "published": "2016-10-13T05:11:04.000Z",
  "updated": "2016-10-13T05:11:04.000Z",
  "title": "Replica Symmetry Breaking without replicas",
  "authors": [
    "Simone Franchini"
  ],
  "comment": "24 pages",
  "categories": [
    "cond-mat.stat-mech"
  ],
  "abstract": "We discuss the concept of pure state of the Replica Symmetry Breaking ansatz in finite and infinite spin systems without averaging on the disorder, nor using replicas. Consider a system of $n$ spins $\\sigma\\in\\Omega^{n}$ with the usual set $\\Omega=\\left\\{ -1,1\\right\\}$ of inner states and let $\\mu:\\,\\Omega^{n}\\rightarrow\\left[0,1\\right]$ a probability measure on it (also random). We interpret the pure states as components of a nontrivial partition of $\\Omega^{n}$ such that the measure conditioned to each component behaves like a product measure. Starting from such definition we are able to derive a very general variational principle. Then we reinterpret the assumptions of the RSB scheme to define a sequence of approximated probability measure and, finally, we apply our results to the Sherrington-Kirkpatrick model to obtain the Parisi formula.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-10-13T05:11:04.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "82D30",
      "60F10"
    ],
    "keywords": [
      "pure state",
      "probability measure",
      "general variational principle",
      "infinite spin systems",
      "replica symmetry breaking ansatz"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}