Localization and quantum percolation

Electronic wave functions are studied on dilute lattices, at dimensionalities 1<~d<~8. Generalized average inverse participation ratios are expanded in powers of the bond concentration, p. Dlog Padé approximants indicate that these ratios diverge as (pq-p)γq, signaling the appearance of extended states for p>pq. These Anderson transitions occur above classical percolation. No divergence is detected at d=2. These results are consistent with the existence of localized states at the center of the band.