Effective plasma model for the level correlations at the mobility edge

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Abstract
We consider the mapping of the energy level statistics for a d-dimensional disordered electron system at the mobility edge between metallic and insulating phases onto the model of a classical one-dimensional 'plasma' of fictitious particles. We deduce the effective pairwise interaction in the plasma that is consistent with the known universal two-level correlation function at the mobility edge and show that for level separation epsilon >> Delta it decreases as ( Delta / epsilon )gamma where Delta is the mean-level spacing, and gamma is the critical exponent related to the known critical exponent v of the correlation length as gamma =1-(vd)-1. We apply the plasma model to generalize Wigner's semicircle law, and to derive the large-energy asymptotic form of the nearest-level distribution. In the limit gamma to 0, which corresponds to the original Dyson mapping onto the plasma with logarithmic repulsion, we recover the classical results of Wigner-Dyson random matrix theory.

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