Fractal Dimensions of Confined Clusters in Two-Dimensional Directed Percolation
Statistical Mechanics
2009-10-22 v4
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.
Keywords
Cite
@article{arxiv.cond-mat/9408076,
title = {Fractal Dimensions of Confined Clusters in Two-Dimensional Directed Percolation},
author = {C. Kaiser and L. Turban},
journal= {arXiv preprint arXiv:cond-mat/9408076},
year = {2009}
}
Comments
6 pages, Plain TeX file, epsf, 3 postscript-figures