Anomalous dynamic scaling of the non-local growth equations

The anomalous dynamic scaling behavior of the d+1 dimensional non-local growth equations is investigated based on the scaling approach. The growth equations studied include the non-local Kardar-Parisi-Zhang (NKPZ), non-local Sun-Guo-Grant (NSGG), and non-local Lai-Das Sarma-Villain (NLDV) equations. The anomalous scaling exponents in both the weak- and strong-coupling regions are obtained, respectively. Our results show that non-local interactions can affect anomalous scaling properties of surface fluctuations.