{
  "id": "cond-mat/9712208",
  "version": "v1",
  "published": "1997-12-17T14:20:26.000Z",
  "updated": "1997-12-17T14:20:26.000Z",
  "title": "On the 1/D expansion for directed polymers",
  "authors": [
    "Giorgio Parisi",
    "Frantisek Slanina"
  ],
  "comment": "Latex, 16 pages, 3 figures",
  "categories": [
    "cond-mat.dis-nn",
    "cond-mat.stat-mech"
  ],
  "abstract": "We present a variational approach for directed polymers in $D$ transversal dimensions which is used to compute the corrections to the mean field theory predictions with broken replica symmetry. The trial function is taken to be a symmetrized version of the mean-field solution, which is known to be exact for $D=\\infty$. We compute the free energy corresponding to that function and show that the finite-$D$ corrections behave like $D^{-4/3}$. It means that the expansion in powers of 1/D should be used with great care here. We hope that the techniques developed in this note will be useful also in the study of spin glasses.",
  "revisions": [
    {
      "version": "v1",
      "updated": "1997-12-17T14:20:26.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "directed polymers",
      "mean field theory predictions",
      "broken replica symmetry",
      "spin glasses",
      "variational approach"
    ],
    "note": {
      "typesetting": "LaTeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "1997cond.mat.12208P"
    }
  }
}