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We implement an efficient strong-disorder renormalization-group (SDRG)procedure to study disordered tight-binding models in any dimension and on theErdos-Renyi random graphs, which represent an appropriate infinite dimensionallimit. Our SDRG algorithm is based on a judicious elimination of most(irrelevant) new bonds generated under RG. It yields excellent agreement withexact numerical results for universal properties at the critical point withoutsignificant increase of computer time, and confirm that, for Andersonlocalization, the upper critical dimension duc = infinite. We find excellentconvergence of the relevant 1/d expansion down to d=2, in contrast to theconventional 2+epsilon expansion, which has little to say about what happens inany d>3. We show that the mysterious mirror symmetry of the conductance scalingfunction is a genuine strong-coupling effect, as speculated in early work. Thisopens an efficient avenue to explore the critical properties of Andersontransition in the strong-coupling limit in high dimensions.

Strong-disorder renormalization group study of the Anderson localization transition in three and higher dimensions