Lack of self-affinity and anomalous roughening in growth processes

We study anomalous scaling properties of growing interfaces in random media. We contrast analytical results of a variety of growth models involving subdiffusion, thermal noise, and quenched disorder with simulations. In these models the interface may be not self-affine and the standard scaling of Family-Vicsek fails. In our two-dimensional models, self-affine surfaces only appear when the roughness exponent is chi = 1/2 or chi = 1. A different scaling picture, which leads to more suitable ways of determining the scaling exponents, is proposed for kinetic roughening when lack of self-affinity exists.