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

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(β) at early time t and becomes saturated at L(α) for t >> L(z), where L is the system size. We obtain β ≈ 0.0788, α ≈ 0.377 for a Sierpinski gasket, and β ≈ 0.100, α ≈ 0.516 for a checkerboard fractal. The dynamic exponent z ≈ 4.79 for a Sierpinski gasket and z ≈ 5.16 for a checkerboard fractal are obtained by the relation z = α/β. They satisfy the scaling relations 4 α + 2 d(f) = z and z = 2 z(rw), where z(rw) is the random-walk exponent of the fractal substrate. A fractional Langevin equation is introduced to describe the model.