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

Abstract

We describe the critical behavior of the Anderson-like transition predicted to occur in the2D tight-binding model with isotropic scale-free long-range correlated disordercharacterized by a power-law spectral density. We explore the scale invarianceof the participation function relative fluctuation at the critical point to locatethe mobility edge as a function of the power-law spectral density exponentα2D. The statesnear the band center, which exhibit power-law localization for uncorrelated disorder, become delocalizedfor α2D>2. In addition, we consider the finite-size scaling hypothesis to estimate thecorrelation length critical exponent. We find that the critical exponentν dependson α2D, thus indicating that correlations in the disorder distribution are indeed relevant in thisregime, in agreement with the extended Harris criterion.