Conformally invariant fractals and potential theory

Conformally invariant fractals and potential theory

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 (straight theta) of the boundary set with local wedge angle straight theta is (straight...

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Veröffentlicht in:Physical review letters 2000-02, Vol.84 (7), p.1363-1367
1. Verfasser: Duplantier, B
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description 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 (straight theta) of the boundary set with local wedge angle straight theta is (straight theta) = pi / straight theta-25-c / 12 (pi-straight theta)(2) / straight theta(2pi-straight theta), with c the central charge of the model. As a corollary, the dimensions D(EP) of the external perimeter and D(H) of the hull of a Potts cluster obey the duality equation (D(EP)-1) (D(H)-1) = 1 / 4. A related covariant MF spectrum is obtained for self-avoiding walks anchored at cluster boundaries.
doi_str_mv 10.1103/PhysRevLett.84.1363
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subjects Condensed Matter
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Other
Physics
title Conformally invariant fractals and potential theory
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