Definition of Percolation Thresholds on Self-Affine Surfaces

Abstract

We study the percolation transition on a two-dimensional substrate with long-range self-affine correlations. We find that the position of the percolation threshold on a correlated lattice is no longer unique and depends on the spanning rule employed. Numerical results are provided for spanning across the lattice in specified (horizontal or vertical), either or both directions. Show more