Distribution of local densities of states, order parameter function, and critical behavior near the Anderson transition

The exact relations between the order parameter function of the Anderson transition and the distributions of local densities of states (LDSO) and eigenfunction amplitudes are derived. It is shown that the non-power-like critical behavior obtained previously in the framework of Bethe lattice (BL) models and effective medium approximation is an artifact of the BL structure and is inconsistent with d-dimensional spatial structure at any d. The critical behavior at finite d is power-like with d= playing the role of an upper critical dimension. Near the transition point, the distribution function of LDOS is very broad and asymmetric.