{
  "id": "cond-mat/0603018",
  "version": "v2",
  "published": "2006-03-01T11:06:02.000Z",
  "updated": "2008-01-24T10:08:34.000Z",
  "title": "Rigorous Inequalities between Length and Time Scales in Glassy Systems",
  "authors": [
    "Andrea Montanari",
    "Guilhem Semerjian"
  ],
  "comment": "24 pages, 3 figures; published version",
  "journal": "J. Stat. Phys. 125, 23 (2006)",
  "doi": "10.1007/s10955-006-9175-y",
  "categories": [
    "cond-mat.stat-mech",
    "cond-mat.dis-nn",
    "math.PR"
  ],
  "abstract": "Glassy systems are characterized by an extremely sluggish dynamics without any simple sign of long range order. It is a debated question whether a correct description of such phenomenon requires the emergence of a large correlation length. We prove rigorous bounds between length and time scales implying the growth of a properly defined length when the relaxation time increases. Our results are valid in a rather general setting, which covers finite-dimensional and mean field systems. As an illustration, we discuss the Glauber (heat bath) dynamics of p-spin glass models on random regular graphs. We present the first proof that a model of this type undergoes a purely dynamical phase transition not accompanied by any thermodynamic singularity.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2008-01-24T10:08:34.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "time scales",
      "glassy systems",
      "rigorous inequalities",
      "long range order",
      "relaxation time increases"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}