Classification of KPZQ and BDP models by multiaffine analysis

We argue differences between the Kardar-Parisi-Zhang with quenched disorder (KPZQ) and the ballistic deposition with power-law noise (BDP) models, using the multiaffine analysis method. The KPZQ and the BDP models show mono-affinity and multiaffinity, respectively. This difference results from the different distribution types of neighbor-height-differences in growth paths. Exponential and power-law distributions are observed in the KPZQ and the BDP, respectively. In addition, we point out the difference of profiles directly, i.e., although the surface profiles of both models and the growth path of the BDP model are rough, the growth path of the KPZQ model is smooth.