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 κc, we find logarithmic growth and logarithmic dependence of the surface width on system size. The amplitude of the correlation function at κc is found to be equal to that observed for roughening at the Kosterlitz-Thouless transition.