Articles dans des revues à comité de lecture
|Surface shape and local critical behaviour in two-dimensional directed percolation|
|Kaiser C., Turban L.|
|Journal of Physics A: Mathematical and General 28 (1995) 351|
|DOI : 10.1088/0305-4470/28/2/012|
|ArXiv : cond-mat/9411077 [PDF]|
|HAL : hal-00422002|
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.