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

C. Kaiser·L. Turban
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Abstract

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=ν_\parallel/νis 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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C. Kaiser, L. Turban. 1997-09-05. Surface Shape and Local Critical Behaviour in Two-Dimensional Directed Percolation. https://doi.org/10.1088/0305-4470%2F28%2F2%2F012

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