Surface Shape and Local Critical Behaviour in Two-Dimensional Directed Percolation

Details Surface Shape and Local Critical Behaviour in Two-Dimensional Directed Percolation Surface Shape and Local Critical Behaviour in Two-Dimensional Directed Percolation

1994-11-18

arxiv.org/abs/cond-mat/9411077v2

J. Phys. A 28 (1995) 351-363

Physics

Condensed Matter

Statistical Mechanics

13 pages, Plain TeX file, epsf, 6 postscript-figures, minor corrections

Scientific paper

10.1088/0305-4470/28/2/012

Two-dimensional directed site percolation is studied in systems directed along the x-axis and limited by a free surface at y=\pm Cx^k. Scaling considerations show that the surface is a relevant perturbation to the local critical behaviour when k<1/z where z=\nu_\parallel/\nu is the dynamical exponent. The tip-to-bulk order parameter correlation function is calculated in the mean-field approximation. The tip percolation probability and the fractal dimensions of critical clusters are obtained through Monte-Carlo simulations. The tip order parameter has a nonuniversal, C-dependent, scaling dimension in the marginal case, k=1/z, and displays a stretched exponential behaviour when the perturbation is relevant. The k-dependence of the fractal dimensions in the relevant case is in agreement with the results of a blob picture approach.

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