NETWORK MODEL OF LOCALIZATION IN A RANDOM MAGNETIC-FIELD

We consider a multichannel network model to study the localization pro blem of noninteracting fermions in a random magnetic field with zero a verage. We argue that the number of channels M is even. After averagin g over the randomness, the network is mapped onto M coupled SU(2N) spi n 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 func tion 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 resul ts and further arguments support the conclusion that all the states ar e localized.