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, W2(t) grows logarithmically at the beginning and becomes saturated at ln L, showing a scaling $${W^2}\left( {L,t} \right) \sim \ln \left[ {{L^{2\alpha }}f\left( {{t \over {{L^z}}}} \right)} \right]$$ with z ≈ 2.0. For the deposition-only model with p = 1, W2(L,t) shows a power law behavior W2(t) ∼ t2β 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.