Restricted Height Model with Conserved Noise

Abstract

We introduce a restricted height model with conservation of the total number of particles. The surface width W(L, t) of our model follows a scaling formula W(2) (L, t) = W(i)(2) - L(2 alpha) f (t/L(z)) as a function of time t, where W(i) and L are an intrinsic width and the system size, respectively. By subtracting the surface width from the intrinsic width, we successfully obtain the roughness exponent alpha approximate to -d(s)/2 and the growth exponent beta approximate to -d(s)/4 for substrate dimensions d(s) = 1, 2, and 3. We also obtain the dynamic exponent z approximate to 2 in all substrate dimensions. The relation between our model and the conserved Edwards-Wilkinson equation is also discussed.