PERCOLATION THROUGH SELF-AFFINE SURFACES

We study the percolation transition in a longe-range correlated system : a self-affine surface. For all relevant physical cases (i.e. positiv e roughness exponents), it is found that the onset of percolation is g overned by the largest wavelength of the height distribution, and thus self-averaging breaks down. Self-averaging is recovered for negative roughness exponents (i.e. power-law decay of the height pair correlati on function) and, in this case, the critical exponents that characteri ze the transition are explicitly dependent on the roughness exponent a bove a threshold value. Below this threshold, the spatial correlations are no longer relevant. The problem is analytically investigated for a hierarchical network and by means of numerical simulations in two di mensions. Finally, we discuss the application of those properties to m ercury porosimetry in cracks.