Quantum Percolation in Magnetic Fields

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, $p_q$. This threshold decreases at small magnetic fields, and shows a periodic dependence on the magnetic flux through a basic plaquette, with period ${\phi }_0=\hslash \frac{c}{e}$. Extended states appear and disappear periodically even at $d=2\mathrm{}$.