Critical behavior of the Hall coefficient near the mobility edge

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Abstract
We analyze the behavior of the Hall conductivity in weak magnetic fields, near the disorder-induced metal-insulator transition. Using the mapping onto the nonlinear σ model we identify a new operator which is relevant to the scaling of the Hall conductivity in weak magnetic fields. Using the Wilson-Polyakov renormalization-group procedure we find that the perturbative behavior of the Hall conductivity, which is observable in two dimensions in the weakly localized regime, is not simply related to the critical behavior of the Hall conductivity. Our theory predicts that the Hall number vanishes at the mobility edge with an exponent g=1 in agreement with several experimental observations.