Scaling approach to the nonlocal surface growth equations

The scaling behavior of nonlocal surface growth equations are analyzed using a Flory-type approach introduced by Hentschel and Family [Phys. Rev. Lett. 66 (1991) 1982]. The growth equations studied include the nonlocal Kardar–Parisi–Zhang, nonlocal Sun–Guo–Grant, and nonlocal Lai–Das Sarma–Villain equation. The types of noise involved include white, colored noise and quenched randomness. We find that the obtained scaling exponents in the weak-coupling region can well match the corresponding results of the dynamic renormalizatin group theory. The scaling exponents in the strong-coupling region are also derived.