Fractal dimensions of confined clusters in two-dimensional directed percolation
- 21 August 1994
- journal article
- Published by IOP Publishing in Journal of Physics A: General Physics
- Vol. 27 (16) , L579-L583
- https://doi.org/10.1088/0305-4470/27/16/003
Abstract
The fractal structure of directed percolation clusters, grown at the percolation threshold inside parabolic-like systems, is studied in two dimensions via Monte Carlo simulations. With a free surface at y=+or-Cxk and a dynamical exponent z, the surface shape is a relevant perturbation when k<1/z and the fractal dimensions of the anisotropic clusters vary continuously with k. Analytic expressions for these variations are obtained using a blob picture approach.Keywords
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