Kardar–Parisi–Zhang universality class of a discrete erosion model

We investigate a novel (d + 1)-dimensional discrete erosion model for d = 1, 2 and 3. The dynamics of the model is controlled by the physically motivated erosion mechanism. The coarse grained nature of this erosion process has been well compared with the Kardar–Parisi–Zhang (KPZ) equation. The kinetic roughening of the discrete model shows the same scaling behavior as that of the KPZ equation in the dimensions d = 1, 2. Moreover, in this present discrete model in (3 + 1)-dimension almost smooth interface has been obtained with vanishingly small roughness exponent, indicating the model belongs to the weak coupling regime of KPZ universality class.