{
  "id": "cond-mat/0208280",
  "version": "v1",
  "published": "2002-08-14T18:07:49.000Z",
  "updated": "2002-08-14T18:07:49.000Z",
  "title": "Replica bounds for optimization problems and diluted spin systems",
  "authors": [
    "Silvio Franz",
    "Michele Leone"
  ],
  "comment": "18 pages, 1 figure",
  "journal": "J. Stat. Phys. 111 (2003) 535-564",
  "categories": [
    "cond-mat.dis-nn",
    "cond-mat.stat-mech"
  ],
  "abstract": "In this paper we generalize to the case of diluted spin models and random combinatorial optimization problems a technique recently introduced by Guerra (cond-mat/0205123) to prove that the replica method generates variational bounds for disordered systems. We analyze a family of models that includes the Viana-Bray model, the diluted p-spin model or random XOR-SAT problem, and the random K-SAT problem, showing that the replica method provides an improvable scheme to obtain lower bounds of the free-energy at all temperatures and of the ground state energy. In the case of K-SAT the replica method thus gives upper bounds of the satisfiability threshold.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2002-08-14T18:07:49.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "diluted spin systems",
      "replica bounds",
      "replica method generates variational bounds",
      "random combinatorial optimization problems"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2002cond.mat..8280F"
    }
  }
}