Conformally Invariant Fractals and Potential Theory
| dc.creator | Duplantier, Bertrand | |
| dc.date | 1999-08-22 | |
| dc.date.accessioned | 2026-07-07T12:33:12Z | |
| dc.date.available | 2026-07-07T12:33:12Z | |
| dc.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 $\hat f(θ)$ of the boundary set with local wedge angle $θ$ is $\hat f(θ)=\fracπθ -\frac{25-c}{12} \frac{(π-θ)^2}{θ(2π-θ)}$, with $c$ the central charge of the model. As a corollary, the dimensions $D_{\rm EP} =sup_θ\hat f(θ)$ of the external perimeter and $D_{\rm H}$ of the hull of a Potts cluster obey the duality equation $(D_{\rm EP}-1)(D_{\rm H}-1)={1/4}$. A related covariant MF spectrum is obtained for self-avoiding walks anchored at cluster boundaries. | |
| dc.description | 5 pages, 1 figure | |
| dc.identifier | https://arxiv.org/abs/cond-mat/9908314 | |
| dc.identifier | http://arxiv.org/abs/cond-mat/9908314 | |
| dc.identifier | Phys.Rev.Lett.84:1363-1367,2000 | |
| dc.identifier | doi:10.1103/PhysRevLett.84.1363 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/217045 | |
| dc.subject | Statistical Mechanics | |
| dc.subject | Mathematical Physics | |
| dc.subject | Probability | |
| dc.title | Conformally Invariant Fractals and Potential Theory | |
| dc.type | text |