Effective Plasma Model for the Level Correlations At the Mobility Edge

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 much greater than 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 nu of the correlation length as gamma = 1-(nu d)(-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 --> 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.