{
  "id": "1002.3261",
  "version": "v1",
  "published": "2010-02-17T13:21:50.000Z",
  "updated": "2010-02-17T13:21:50.000Z",
  "title": "On the convergence of cluster expansions for polymer gases",
  "authors": [
    "Rodrigo Bissacot",
    "Roberto Fernández",
    "Aldo Procacci"
  ],
  "categories": [
    "math-ph",
    "math.MP"
  ],
  "abstract": "We compare the different convergence criteria available for cluster expansions of polymer gases subjected to hard-core exclusions, with emphasis on polymers defined as finite subsets of a countable set (e.g. contour expansions and more generally high- and low-temperature expansions). In order of increasing strength, these criteria are: (i) Dobrushin criterion, obtained by a simple inductive argument; (ii) Gruber-Kunz criterion obtained through the use of Kirkwood-Salzburg equations, and (iii) a criterion obtained by two of us via a direct combinatorial handling of the terms of the expansion. We show that for subset polymers our sharper criterion can be proven both by a suitable adaptation of Dobrushin inductive argument and by an alternative --in fact, more elementary-- handling of the Kirkwood-Salzburg equations. In addition we show that for general abstract polymers this alternative treatment leads to the same convergence region as the inductive Dobrushin argument and, furthermore, to a systematic way to improve bounds on correlations.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-02-17T13:21:50.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "82B20",
      "05A20"
    ],
    "keywords": [
      "cluster expansions",
      "polymer gases",
      "kirkwood-salzburg equations",
      "general abstract polymers",
      "direct combinatorial"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "doi": "10.1007/s10955-010-9956-1",
      "journal": "Journal of Statistical Physics",
      "year": 2010,
      "month": "May",
      "volume": 139,
      "number": 4,
      "pages": 598
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010JSP...139..598B"
    }
  }
}