Critical behavior of the two-dimensional Anderson model with long-range correlated disorder

We describe the critical behavior of the Anderson-like transition predicted to occur in the 2D tight-binding model with isotropic scale-free long-range correlated disorder characterized by a power-law spectral density. We explore the scale invariance of the participation function relative fluctuation at the critical point to locate the mobility edge as a function of the power-law spectral density exponent alpha(2D). The states near the band center, which exhibit power-law localization for uncorrelated disorder, become delocalized for alpha(2D) > 2. In addition, we consider the finite-size scaling hypothesis to estimate the correlation length critical exponent. We find that the critical exponent. depends on alpha(2D), thus indicating that correlations in the disorder distribution are indeed relevant in this regime, in agreement with the extended Harris criterion.