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 $\alpha \simeq {\alpha }_{\mathrm{loc}}<{\alpha }_s$ in (1+1) dimensions, which is beyond the existing dynamic scaling classifications.

• Received 21 August 2020
• Revised 22 December 2020
• Accepted 23 December 2020

DOI:https://doi.org/10.1103/PhysRevE.103.012121