Effects of Scale-Free Disorder on the Anderson Metal-Insulator Transition

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We investigate the three-dimensional Anderson model of localization via a modified transfer-matrix method in the presence of scale-free diagonal disorder characterized by a disorder correlation function g(r) decaying asymptotically as r⁻α. We study the dependence of the localization-length exponent ν on the correlation-strength exponent α. % For fixed disorder W, there is a critical α c, such that for α< α c, ν=2/α and for α> α c, ν remains that of the uncorrelated system in accordance with the extended Harris criterion. At the band center, ν is independent of α but equal to that of the uncorrelated system. The physical mechanisms leading to this different behavior are discussed.