Localization transition in media with anisotropic diagonal disorder

Localization behavior of the Anderson model with anisotropic diagonal disorder is both simulated numerically and calculated diagrammatically. As a function of the anisotropy parameter θ that interpolates between a one-dimensional randomly layered system and three-dimensional isotropic randomness, our results indicate the existence of a critical ${\mathrm{\theta }}_{\mathrm{c}}$ below which the wave function is localized even for infinitesimal values of randomness. Implications for observing the mobility edge in random superlattices are discussed.