Restricted Solid-on-Solid Model with Various Deposition and Evaporation Probability on d=4+1 dimensions

Abstract

We control the deposition probability p (the evaporation probability 1- p) in a restricted solid-on-solid model and monitor the surface width W(L,t) as a function of time t, where L is the system size in d = 4 + 1 dimensions. At p = 1/2, the surface becomes flat, following the Edwards and Wilkinson universality class. At p = 0.88, W-2(t) grows logarithmically at the beginning and becomes saturated at In L, showing a scaling W-2(L,t) similar to ln [L-2a f (t/L-z)] with z approximate to 2.0. For the deposition-only model with p = 1, W-2(L, t) shows a power law behavior W-2(t) similar to t2 beta with a rough interface. With varying p, a smooth-to-rough surface transition is found, implying that d = 4 + 1 is not the upper critical dimension of the Kardar Parisi Zhang equation.