Surface growth on percolation networks by a conserved-noise restricted solid-on-solid growth model

Surface growth by the conserved-noise restricted solid-on-solid model is investigated on diluted lattices, i.e., on percolation networks that are embedded in two spatial dimensions. The growth exponent β and the roughness exponent α are defined, respectively, by the mean-square surface width via W(2)(t)∼t(2β) and the mean-square saturated width via W(sat)(2)(L)∼L(2α), where L is the system size. These are measured on both an infinite network and a backbone network and the results are compared with power-counting predictions obtained using the fractional Langevin equation. While the Monte Carlo results on deterministic fractal substrates show excellent agreement with the predictions [D. H. Kim and J. M. Kim, Phys. Rev. E 84, 011105 (2011)], the results on critical percolation networks deviate by 8%-12% from these predictions.