Extensive numerical simulations of surface growth with temporally correlated noise

Surface growth processes can be significantly affected by long-range temporal correlations. In this work, we perform extensive numerical simulations of a (1+1)- and (2+1)-dimensional ballistic deposition (BD) model driven by temporally correlated noise, which is regarded as the temporal correlated Kardar-Parisi-Zhang universality class. Our results are compared with the existing theoretical predictions and numerical simulations. When the temporal correlation exponent is above a certain threshold, BD surfaces develop gradually faceted patterns. We find that the temporal correlated BD system displays nontrivial dynamic properties, and the characteristic roughness exponents satisfy $\ensuremath{\alpha}\ensuremath{\simeq}{\ensuremath{\alpha}}_{\mathrm{loc}}l{\ensuremath{\alpha}}_{s}$ in (1+1) dimensions, which is beyond the existing dynamic scaling classifications.