Equilibrium-restricted solid-on-solid growth model on fractal substrates

The equilibrium-restricted solid-on-solid growth model on fractal substrates is studied by introducing a fractional Langevin equation. The growth exponent beta and the roughness exponent alpha defined, respectively, by the surface width via W approximately t(beta) and the saturated width via W(sat) approximately L(alpha), L being the system size, were obtained by a power-counting analysis, and the scaling relation 2alpha+d(f)=z(RW) was found to hold. The numerical simulation data on Sierpinski gasket, checkerboard fractal, and critical percolation cluster were found to agree well with the analytical predictions of the fractional Langevin equation.