{
  "id": "cond-mat/0004321",
  "version": "v1",
  "published": "2000-04-19T03:34:35.000Z",
  "updated": "2000-04-19T03:34:35.000Z",
  "title": "Critical exponents of plane meanders",
  "authors": [
    "Iwan Jensen",
    "Anthony J Guttmann"
  ],
  "comment": "8 pages, 4 eps figures",
  "categories": [
    "cond-mat.stat-mech",
    "math-ph",
    "math.MP"
  ],
  "abstract": "Meanders form a set of combinatorial problems concerned with the enumeration of self-avoiding loops crossing a line through a given number of points, $n$. Meanders are considered distinct up to any smooth deformation leaving the line fixed. We use a recently developed algorithm, based on transfer matrix methods, to enumerate plane meanders. This allows us to calculate the number of closed meanders up to $n=48$, the number of open meanders up to $n=43$, and the number of semi-meanders up to $n=45$. The analysis of the series yields accurate estimates of both the critical point and critical exponent, and shows that a recent conjecture for the exact value of the semi-meander critical exponent is unlikely to be correct, while the conjectured exponent value for closed and open meanders is not inconsistent with the results from the analysis.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2000-04-19T03:34:35.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "critical exponent",
      "series yields accurate estimates",
      "open meanders",
      "enumerate plane meanders",
      "transfer matrix methods"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2000cond.mat..4321J"
    }
  }
}