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We examine the effect of long-range spatially correlated disorder on the Anderson localization transition in d=2+ dimensions. This is described as a phase transition in an appropriate non-linear model. We consider a model of scalar waves in a medium with an inhomogeneous index of refraction characterized by scattering strength ^2 and spatial correlations of range a decaying (i) exponentially ₁^2a^-de^-x{a} and (ii) by power laws ₂^2 ({a^2+x^2) }^-m (m>0). A replica-field-theory representation is utilized in the calculation of the one- and two-particle Green's functions. In addition to the usual diffusive Goldstone mode of the field theory arising from energy conservation, the non-linear model is shown to possess a discrete spectrum of low-lying nondiffusive modes associated with approximate wave-vector (k) conservation in the geometric optics limit ka1. For waves it is shown that all states are localized for d2 with diverging localization lengths in the low-frequency limit and that the mobility edge in d=2+ separating high-frequency, localized states from low-frequency, extended states is characterized by the same critical exponents as for spatially uncorrelated disorder provided m>. The problem of electron localization in a long-range correlated random potential is also described within the same universality class.
John et al. (Thu,) studied this question.