Phase transition in a restricted solid-on-solid surface-growth model in 2+1 dimensions

A generalization of the restricted solid-on-solid growth model of Kim and Kosterlitz is studied and found to exhibit a phase transition, as a function of a temperaturelike parameter κ, in 2+1 dimensions. The surface-width exponents cross over from the Kim-Kosterlitz values for small κ, to the low-temperature values α≊0.25, β≊0.14 for large κ. At the transition point ${\kappa }_c$, we find logarithmic growth and logarithmic dependence of the surface width on system size. The amplitude of the correlation function at ${\kappa }_c$ is found to be equal to that observed for roughening at the Kosterlitz-Thouless transition.