A restricted curvature model on a Sierpinski gasket substrate

Abstract

The surface structure of an equilibrium restricted curvature (RC) model on a Sierpinski gasket substrate is studied. The surface width W increases as t(beta) at early time t and becomes saturated at L-alpha for t >> L-z, where L is the system size. The growth exponent beta approximate to 0.323, the roughness exponent alpha approximate to 1.54 and the dynamic exponent z approximate to 4.78 are obtained numerically. They satisfy the scaling relations 2 alpha+ d(f) = z and z = 2z(rw) very well, where z(rw) is the random walk exponent of the Sierpinski gasket. We introduce a fractional Langevin equation to describe the model.