Stochastic equation for conserved growth in a restricted solid-on-solid model

We apply the master-equation method naturally extended for the nonlocal growth process to directly deriving the continuum stochastic equation for a conserved growth model with a restricted solid-on-solid condition. The Villain-Lai–Das Sarma growth equation we obtain for the model is consistent with the result of recent numerical simulations. Furthermore, we find that only the relaxation of the deposited particles up to the nearest neighborhood for N=1 condition or the next-nearest neighborhood for N>1 condition determines the scaling property and the universality class of the model, and the higher-neighbor hopping processes play no essential role. The choice of the regularization scheme in the derivation procedure is also discussed.