Restricted Solid-on-solid Growth Model for Fractal Substrates

A restricted solid-on-solid growth model is studied for various fractal substrates, i.e., a Sierpinski gasket, a checkerboard fractal, and a Sierpinski carpet, all embedded in two dimensions. The interface width W grows as t(beta) with beta approximate to 0.29 for Sierpinski gasket and beta approximate to 0.31 for both a checkerboard fractal and a Sierpinski carpet. At saturation, W follows W similar to L-alpha, with alpha approximate to 0.50 for a Sierpinski gasket and alpha approximate to 0.52 for both a checkerboard fractal and a Sierpinski carpet, where L is the system size. The dynamic exponent z is obtained from the relation z = alpha/beta. The estimated exponents break the scaling relation alpha + z = 2, which is known to be valid on a regular lattice.