Effects of spin interactions in disordered electronic systems: Loop expansions and exact relations among local gauge invariant models

Spindependent ensembles for disordered electronic systems are examined in the region of extended states. We derive relations between spindependent and previously studied spinless ensembles. We prove that these relations are valid in all orders of a graph theory, on the basis of which we propose them to be exact. These exact relations and supplementary two loop order calculations in 2+ dimensions are used to reveal the existence of universality classes for the critical behaviour at the mobility edges. The mobility edge behaviour of a spindependent ensemble with real (random) hopping agrees with that of the spinless phase invariant ensemble except for a crossover to the real matrix ensemble in the limit of vanishing spinflip amplitudes. Anomalous properties in the band center are also discussed. We derive a transformation which maps arbitrary correlation functions of a complex spindependent ensemble into those of the real matrix ensemble. This relation implies the absence of a mobility edge for the complex spindependent ensemble within the validity region of the theory.