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

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.

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

References in corpus (5)

• SCHRÖdinger Invariance and Strongly Anisotropic Critical Systems
• Inhomogeneous Systems with Unusual Critical Behaviour
• Anisotropic critical phenomena in parabolic geometries: the directed self-avoiding walk
• Critical behaviour in parabolic geometries
• Fractal Dimensions of Confined Clusters in Two-Dimensional Directed Percolation

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• Hard core particle exclusion effects in low dimensional non-equilibrium phase transitions
• Boundary-induced nonequilibrium phase transition into an absorbing state
• Critical behavior of the two dimensional 2A->3A, 4A->0 binary system
• Viscoelastic Interfaces Driven in Disordered Media and Applications to Friction
• Simplest nonequilibrium phase transition into an absorbing state
• Tuning spreading and avalanche-size exponents in directed percolation with modified activation probabilities
• Universal crossing probability in anisotropic systems