The Anderson metal-insulator transition in the presence of scale-free disorder

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(-alpha). We study the dependence of the localization length exponent nu on the correlation strength exponent alpha. For fixed disorder W, there is a critical alpha(c), such that for alpha<alpha(c), nu=2/alpha and for alpha>alpha(c),. nu remains that of the uncorrelated system in accordance with the extended Harris criterion. At the band center, nu is independent of alpha but equal to that of the uncorrelated system. The physical mechanisms leading to this different behavior are discussed.