We investigate the time evolution of the roughness of Kadar–Parisi–Zhang (KPZ) equation in (2+1) dimensions. Scaling behavior of the roughness is analyzed from scale transformations and the scaling function is obtained from numerical simulations.

In order to estimate roughness exponents of interface growth models, we propose the calculation of effective exponents from the roughness fluctuation σ in the steady state. We compare the finite-size behavior of these exponents and the ones calculated from the average roughness 〈w2〉 for two...

Interface pinning–depinning transition in quenched random media is studied by investigating a simple directed polymer model with external driving force F. The directed polymer model can be described by a quenched Kardar–Parisi–Zhang (KPZ) equation. In our model, the velocity on a tilted...