Field theory of the random flux model

The random flux model (defined here as a model of lattice fermions hopping under the influence of maximally random link disorder) is analysed field th eoretically. It is shown that the long range physics of the model is descri bed by the supersymmetric version of a field theory that has been derived e arlier in connection with lattice fermions subject to weak random hopping. More precisely, the field theory relevant for the behaviour of n-point corr elation functions is of non-linear sigma model type, where the group GL(n \ n) is the global invariant manifold. Tt is argued that the model universal ly describes the long range physics of random phase fermions and provides f urther evidence in favour of the existence of delocalised states in the: mi ddle of the band in two dimensions. The same formalism is applied to the st udy of non-Abelian generalisations of the random flux model, i.e. N-compone nt fermions whose hopping is mediated by random U(N) matrices. We discuss s ome physical applications of these models and: argue that, for sufficiently large N, the existence of long range correlations in the band centre (equi valent to metallic behaviour in the Abelian case) can be safely deduced fro m the RG analysis of the model. (C) 1999 Elsevier Science B.V. All rights r eserved.