Continuous Height-restricted Solid-on-solid Model in Higher Dimensions

A continuous height-restricted solid-on-solid model is introduced to reduce the artifact of the discrete height model. The interface width W(t) grows as t(beta) at the beginning and becomes saturated with L-alpha for t >> L-z, where z is the dynamic exponent. Through a numerical simulation of the model, the growth exponent beta for dimension d = 4 + 1, 5 + 1, 6 + 1, and 7 + 1 and the roughness exponent alpha for d = 4 + 1 and 5 + 1 are obtained. They satisfy the scaling relation alpha + z = 2 very well for both d = 4+ 1 and d = 5 + 1. Our results show that the upper critical dimension of the Kardar-Parisi-Zhang equation is higher than d = 7 + 1.