Phase transition of generalized restricted solid-on-solid model in d=5+1 dimension

Abstract

We control the nonlinearity of a restricted solid-on-solid growth model by adjusting the deposition probability p, and find a rough-to-smooth surface transition in the d = 5 + 1 dimension. At the critical probability pc, the standard deviation of the surface height W-2(t) grows as W-2(t) similar to ln t at the beginning and becomes saturated at W-2(L) similar to ln L at the later time t >> L-2, where L is the system size of the substrate. The width follows a scaling form of W-2(L,t) similar to ln [L(2a)g(t/L-z)], with the dynamic exponent z approximate to 1.97, which is consistent with z = 2. Our results imply that the upper critical dimension of the Kardar-Parisi-Zhang equation is higher than the d = 5 + 1 dimension.