We discuss here in detail a new analytical random walk approach to calculating the phase diagram for spatially extended systems with multiplicative noise. We use the Anderson localization problem as an example. The transition from delocalized to localized states is treated as a generalized...

Our previous results [V.N. Kuzovkov, W. von Niessen, V. Kashcheyevs, O. Hein, J. Phys. Condens. Matter 14 (2002) 13777] dealing with the analytical solution of the two-dimensional (2-D) Anderson localization problem due to disorder is generalized for anisotropic systems (two different hopping...