Fractal Dimensions of Confined Clusters in Two-Dimensional Directed Percolation

Details Fractal Dimensions of Confined Clusters in Two-Dimensional Directed Percolation Fractal Dimensions of Confined Clusters in Two-Dimensional Directed Percolation

1994-08-24

arxiv.org/abs/cond-mat/9408076v4

J. Phys. A 27 (1994) L579

Physics

Condensed Matter

Statistical Mechanics

6 pages, Plain TeX file, epsf, 3 postscript-figures

Scientific paper

10.1088/0305-4470/27/16/003

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=\pm Cx^k 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.

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