Restricted height discrete model

We introduce a discrete growth model following the Edward- Willikinson equation with a conservative noise. The surface width $W(h,t)$ of our model follows $W^2(L,t)=W_i^2- L^{2\alpha}f(t/L^z)$, where $W_i$ is an intrinsic width. By subtracting the surface width from the intrinsic width, the roughness exponent $\alpha \approx -d_s/2$ and the growth exponent $\beta \approx -d_s/4$ are successfully obtained for the substrate dimension $d_s=1, 2$ and $3$. Various discrete models with conserved noise are also discussed.