Fractal Dimensions of Confined Clusters in Two-Dimensional Directed Percolation

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=\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.

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

References in corpus (3)

• Inhomogeneous Systems with Unusual Critical Behaviour
• Anisotropic critical phenomena in parabolic geometries: the directed self-avoiding walk
• Critical behaviour in parabolic geometries

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