Surface Diffusion in the Solid-on-Solid Model

Abstract

We present results in $1+1$ and $2+1$ dimensions for surface diffusion controlled profile relaxation for the solid-on-solid model above and below the roughening transition. For all cases examined we found that the characteristic time scale $\ensuremath{\tau}$ for the decay of a sinusoidal profile scaled with the wavelength $L$ as $\ensuremath{\tau}\ensuremath{\sim}{L}^{z}$ where $z\ensuremath{\cong}4$. These results can be understood in terms of the anomalous diffusion displayed by tracer atoms whose root mean square displacement scaled as ${t}^{1/4}$.