Dynamic scaling and phase transitions in interface growth

Abstract

The dynamic scaling approach is an effective tool for understanding the temporal evolution of fluctuating interfaces. The surface width w obeys the scaling form w(L, t)=L αƒ(t/L α β , where α and β are exponents which characterize how the surface width grows with the length scale L and the time t. Applications of dynamic scaling to a number of surface growth models are discussed. The results of a large-scale simulation of the ballistic deposition model in three dimensions are presented and compared with recent conjectures. The question of universality in interface growth is addressed and a finite temperature generalization of the restricted solid-on-solid model is studied. This model appears to undergo a phase transition from the usual rough phase at high temperatures to a new phase at low temperatures. Numerical solutions of the generalized Langevin equation indicate that there is no phase transition in 2+1 dimensions. Thus, the relation between the continuum equation and the discrete models is still an open question.