  Scattering theoretical network models for general coherent wave mechanical
systems with quenched disorder are investigated. We focus on universality
classes for two dimensional systems with no preferred orientation: Systems of
spinless waves undergoing scattering events with broken or unbroken time
reversal symmetry and systems of spin 1/2 waves with time reversal symmetric
scattering. The phase diagram in the parameter space of scattering strengths is
determined. The model breaking time reversal symmetry contains the critical
point of quantum Hall systems but, like the model with unbroken time reversal
symmetry, only one attractive fixed point, namely that of strong localization.
Multifractal exponents and quasi-one-dimensional localization lengths are
calculated numerically and found to be related by conformal invariance.
Furthermore, they agree quantitatively with theoretical predictions. For
non-vanishing spin scattering strength the spin 1/2 systems show
localization-delocalization transitions.
