We investigate analytically the large dimensional behavior of the Kardar-Parisi-Zhang (KPZ) dynamics of surface growth using a recently proposed nonperturbative renormalization for self-affine surface dynamics. Within this framework, we show that the roughness exponent α decays not faster than $\alpha \sim 1/d$ for large $d.\mathrm{}$ This implies the absence of a finite upper critical dimension.

• Received 7 April 1998

DOI:https://doi.org/10.1103/PhysRevE.58.R5209