Determination of universality classes for spin-dependent ensembles with time-reversal invariance

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Abstract
The critical localisation behaviour of spin-dependent local gauge-invariant models with time-reversal invariance is exactly classified in terms of universality classes. Exact means valid in all orders of the 2+ epsilon expansion. The corresponding symmetries are determined field-theoretically. In particular, the authors extend in a certain approximation, which becomes exact at the critical point the recently found relations between the spin-dependent phase-invariant ensemble and the real matrix ensemble on the one hand and between the spin-dependent real matrix ensemble and the phase-invariant ensemble on the other.