A generalized average inverse participation ratio, for the one-electron wave functions of a dilute tight-binding model on a d dimensional hypercubic lattice, is studied at finite magnetic fields. Extended wave functions appear above a quantum threshold bond concentration, pq. This threshold decreases at small magnetic fields, and shows a periodic dependence on the magnetic flux through a basic plaquette, with period φ₀=c/e. Extended states appear and disappear periodically even at $d=2$.
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Meir et al. (1986) studied this question.
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