Conserved noise restricted-solid-on-solid model on fractal substrates

Abstract

A conserved noise restricted solid-on-solid model on both a Sierpinski gasket substrate and a checkerboard fractal substrate is studied. The interface width W grows as t(beta) at early time t and becomes saturated at L-alpha for t >> L-z, where L is the system size. We obtain beta approximate to 0.0788, alpha approximate to 0.377 for a Sierpinski gasket, and beta approximate to 0.100, alpha approximate to 0.516 for a checkerboard fractal. The dynamic exponent z approximate to 4.79 for a Sierpinski gasket and z approximate to 5.16 for a checkerboard fractal are obtained by the relation z = alpha/beta. They satisfy the scaling relations 4 alpha + 2d(f) = z and z = 2z(rw), where z(rw) is the random-walk exponent of the fractal substrate. A fractional Langevin equation is introduced to describe the model.