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

Two-dimensional directed site percolation is studied in systems direct ed along the x-axis and limited by a free surface at y = +/- Cx(k). Sc aling 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 correlat ion function is calculated in the mean-held approximation. The tip per colation probability and the fractal dimensions of critical clusters a re obtained through Monte Carlo simulations. The tip order parameter h as anon-universal, C-dependent, scaling dimension in the marginal case , k = 1/z, and displays a stretched exponential behaviour when the per turbation is relevant. The k-dependence of the fractal dimensions in t he relevant case is in agreement with the results of a blob picture ap proach.