{
  "id": "cond-mat/0111374",
  "version": "v2",
  "published": "2001-11-20T15:08:14.000Z",
  "updated": "2002-01-30T18:30:22.000Z",
  "title": "A Transfer Matrix for the Backbone Exponent of Two-Dimensional Percolation",
  "authors": [
    "J. L. Jacobsen",
    "P. Zinn-Justin"
  ],
  "comment": "19 pages",
  "journal": "J. Phys. A 35 (2002), 2131--2144",
  "doi": "10.1088/0305-4470/35/9/304",
  "categories": [
    "cond-mat.stat-mech"
  ],
  "abstract": "Rephrasing the backbone of two-dimensional percolation as a monochromatic path crossing problem, we investigate the latter by a transfer matrix approach. Conformal invariance links the backbone dimension D_b to the highest eigenvalue of the transfer matrix T, and we obtain the result D_b=1.6431 \\pm 0.0006. For a strip of width L, T is roughly of size 2^{3^L}, but we manage to reduce it to \\sim L!. We find that the value of D_b is stable with respect to inclusion of additional ``blobs'' tangent to the backbone in a finite number of points.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2002-01-30T18:30:22.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "two-dimensional percolation",
      "backbone exponent",
      "monochromatic path crossing problem",
      "transfer matrix approach",
      "conformal invariance links"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}