  The random flux model (defined here as a model of lattice fermions hopping
under the influence of maximally random link disorder) is analysed field
theoretically. It is shown that the long range physics of the model is
described by the supersymmetric version of a field theory that has been derived
earlier in connection with lattice fermions subject to weak random hopping.
More precisely, the field theory relevant for the behaviour of n-point
correlation functions is of non-linear sigma model type, where the group
GL(n|n) is the global invariant manifold. It is argued that the model
universally describes the long range physics of random phase fermions and
provides further evidence in favour of the existence of delocalised states in
the middle of the band in two dimensions. The same formalism is applied to the
study of non-Abelian generalisations of the random flux model, i.e. N-component
fermions whose hopping is mediated by random U(N) matrices. We discuss some
physical applications of these models and argue that, for sufficiently large N,
the existence of long range correlations in the band center (equivalent to
metallic behaviour in the Abelian case) can be safely deduced from the RG
analysis of the model.
