Random Walk Diffusion Model with a Restricted Solid-on-Solid Condition in Higher Dimensions

Abstract

We study a random walk diffusion model under the restricted solid-on-solid (RSOS) condition in d = 3 + 1 and d = 4 + 1 dimensions. A dropped particle is allowed to take a random walk until satisfying the RSOS condition. The surface width W increases as t(beta) in early time with beta = 0.081 +/- 0.006 and becomes saturated at L-alpha with alpha = 0.29 +/- 0.03 in d = 3 + 1. In d = 4 + 1, W (t) grows as 2b ln t at the beginning and becomes saturated at 2a ln L The dynamic exponent z approximate to 3.79 is obtained from the relation z=a/b. This value is slightly less than, but consistent with, the value obtained from the related Langevin equation. Our results imply that the upper critical dimension of the model is d =4+1.