Abstract
The multifractal (MF) distribution of the electrostatic potential near any conformally invariant fractal boundary, like a critical loop or a -state Potts cluster, is solved in two dimensions. The dimension of the boundary set with local wedge angle is , with the central charge of the model. As a corollary, the dimensions of the external perimeter and of the hull of a Potts cluster obey the duality equation . 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