Dynamics of Growing Interfaces in Disordered Medium: The Effect of Lateral Growth

We study the model of a driven interface in a disordered medium including the KPZ-nonlinearity. The coupled functional renormalization group flow equations for the disorder correlator and the coupling constant associated with the KPZ-nonlinearity possess a strong coupling fixed-point for the interface dimensions $d=1$, 2. In $d=1$ we get the roughness exponent and the dynamical exponent in one-loop approximation respectively as $\zeta = 0.8615$ and $z=1$