Conformally Invariant Fractals and Potential Theory

Bertrand Duplantier
Phys. Rev. Lett. 84, 1363 – Published 14 February 2000
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Abstract

The multifractal (MF) distribution of the electrostatic potential near any conformally invariant fractal boundary, like a critical O(N) loop or a Q-state Potts cluster, is solved in two dimensions. The dimension f^(θ) of the boundary set with local wedge angle θ is f^(θ)=πθ25c12(πθ)2θ(2πθ), with c the central charge of the model. As a corollary, the dimensions DEP of the external perimeter and DH of the hull of a Potts cluster obey the duality equation (DEP1)(DH1)=14. A related covariant MF spectrum is obtained for self-avoiding walks anchored at cluster boundaries.

  • Received 19 August 1999

DOI:https://doi.org/10.1103/PhysRevLett.84.1363

©2000 American Physical Society

Authors & Affiliations

Bertrand Duplantier

  • Service de Physique Théorique de Saclay, F-91191 Gif-sur-Yvette Cedex, France
  • Institut Henri Poincaré, 11 rue Pierre et Marie Curie, 75231 Paris Cedex 05, France
  • and Isaac Newton Institute for Mathematical Sciences, 20 Clarkson Road, Cambridge CB3 OHE, United Kingdom

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Issue

Vol. 84, Iss. 7 — 14 February 2000

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