{
  "id": "cond-mat/0207743",
  "version": "v1",
  "published": "2002-07-31T17:52:28.000Z",
  "updated": "2002-07-31T17:52:28.000Z",
  "title": "Higher Conformal Multifractality",
  "authors": [
    "Bertrand Duplantier"
  ],
  "comment": "38 pages, 7 figures. Review article written for the Rutgers meeting, held in celebration of Michael E. Fisher's 70th birthday, to appear in J. Stat. Phys",
  "categories": [
    "cond-mat.stat-mech"
  ],
  "abstract": "We derive, from conformal invariance and quantum gravity, the multifractal spectrum f(alpha,c) of the harmonic measure (or electrostatic potential, or diffusion field) near any conformally invariant fractal in two dimensions, corresponding to a conformal field theory of central charge c. It gives the Hausdorff dimension of the set of boundary points where the potential varies with distance r to the fractal frontier as r^{alpha}. First examples are a Brownian frontier, a self-avoiding walk, or a percolation cluster. Potts, O(N) models, and the so-called SLE process are also considered. Higher multifractal functions are derived, like the universal function f_2(alpha,alpha') which gives the Hausdorff dimension of the points where the potential jointly varies with distance r as r^{alpha} on one side of the random curve, and as r^{alpha'} on the other. We present a duality between external perimeters of Potts clusters and O(N) loops at their critical point, obtained in a former work, as well as the corresponding duality in the SLE_{kappa} process for kappa kappa'=16.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2002-07-31T17:52:28.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "higher conformal multifractality",
      "hausdorff dimension",
      "higher multifractal functions",
      "conformal field theory",
      "multifractal spectrum"
    ],
    "tags": [
      "review article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 38,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 591829,
      "adsabs": "2002cond.mat..7743D"
    }
  }
}