Network model of localization in a random magnetic field

We consider a multichannel network model to study the localization problem of noninteracting fermions in a random magnetic field with zero average. We argue that the number of channels M is even. After averaging over the randomness, the network is mapped onto M coupled SU(2N) spin chains in the N --> 0 limit. In the large conductance limit g = <M(e(2)/2 pi(h)over bar>) (M much greater than 2), it turns out that this system is equivalent to a particular representation of the U(2N)/U(N) x U(N) sigma model (N --> 0) without a topological term. The beta function beta(1/M) of this sigma model in the 1/M expansion is consistent with the previously known beta(g) of the unitary ensemble. These results and further arguments support the conclusion that all the states are localized.