Two-dimensional localization in the presence of random flux and the quantum Hall system at even-denominator filling fractions

We present detailed numerical calculations of the two-dimensional localization problem in the presence of random flux and discuss the implications of these results to the ν=1/2 anomaly in the quantum Hall systems. In the case where flux disorder breaks the time-reversal symmetry, finite-size scaling of the localization length and the conductance are consistent with a finite region of extended states above a critical energy ${\mathit{E}}_{\mathit{c}}$. For the special case of randomly distributed half-flux quanta per plaquette, where time-reversal invariance is preserved, we find no mobility edge at any nonzero ${\mathit{E}}_{\mathit{c}}$. We observe a crossover from positive magnetoresistance to negative magnetoresistance as potential disorder is increased. These results give qualitative explanation of the striking magnetotransport data at even-denominator filling fractions and suggest an experiment to observe the crossover behavior.