Surface growth on diluted lattices by a restricted solid-on-solid model

An influence of diluted sites on surface growth has been investigated, using the restricted solid-on-solid model. It was found that, with respect to equilibrium growth, the surface width and the saturated width exhibited universal power-law behaviors, i.e., W similar to t(beta) and W-sat similar to L-zeta, regarding all cases with respect to the concentration of diluted sites x=1-p, with p being the occupation probability on each lattice site. For x < x(c) (=1-p(c), p(c) being the percolation threshold), the growth appeared to be similar to that of a regular lattice, both in two and three dimensions. For x=x(c), the growth yielded nontrivial exponents which were different from those on a regular lattice. In nonequilibrium growth, a considerable amount of diluted sites (x < x(c)) appeared to yield nonuniversal growth, unlike the case of a regular lattice. The cause of nonuniversal growth dynamics has been investigated, considering the growth on a backbone cluster and on lattices constructed with periodically and randomly diluted subcells.