SURFACE SHAPE AND LOCAL CRITICAL-BEHAVIOR IN 2-DIMENSIONAL DIRECTED PERCOLATION

Two-dimensional directed site percolation is studied in systems directed along the x-axis and limited by a free surface at y = +/- Cx(k). Scaling considerations show that the surface is a relevant perturbation to the local critical behaviour when k < 1/z, where z = v(parallel to)/v is the dynamical exponent. The tip-to-bulk order parameter correlation function is calculated in the mean-held approximation. The tip percolation probability and the fractal dimensions of critical clusters are obtained through Monte Carlo simulations. The tip order parameter has anon-universal, 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.