The roughening transition of interfaces in disordered media

Competing pinning effects on a D-dimensional interface by weak impurity disorder and a periodic potential of the underlying crystal lattice are analyzed for $2<D<4$. We use both the Gaussian variational method (GVM) and the functional renormalization group $\epsilon=4-D$ expansion (FRG) which yield different phase diagrams: Whereas the FRG always predicts a rough phase with irrelevant lattice pinning, the GVM in combination with a three parameter RG for the random potential [T. Nattermann, H. Leschhorn, Europhys. Lett. 16 (1991) 603] leads to a roughening transition of first order. For random bond disorder we compute self-consistently the effective lattice potential.