Surface growth on diluted lattices using a restricted curvature model

Abstract

Surface growth using the equilibrium restricted curvature model was studied on diluted lattices, i.e. on percolation networks, embedded in a square lattice. The growth exponent β and the roughness exponent α were measured on infinite networks for the percolation probability and backbone networks at pc, where pc is the percolation threshold. For p = pc, both the infinite network and backbone network are known to be fractals with fractal dimensions different from each other, whereas for p > pc they are Euclidean. Therefore, our work for p = pc is regarded as the surface growth on random fractal substrates. The results were compared to the predicted results using power counting for the fractional Herring–Mullins equation with a noise restriction modified for the fractal substrates. For p > pc, the exponents appeared to be similar to those for the regular lattice, whereas for p = pc they were consistent with the predictions for both an infinite network and a backbone network. The scaling relation was satisfied for both cases, where df is the fractal dimension of the substrate and z is the dynamic exponent given as .