Mean-field limit of the random flux model
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The problem of non--interacting electrons on a square lattice subject to a random magnetic flux is mapped onto a one--dimensional model with infinitely many orbitals per site. Linking each orbital with $N(\gg1)$ other orbitals maps the problem onto Wegner's $N$-orbital model in the same limit, while the original problem corresponds to $N=1$. The exact solution for $N=\infty$, the mean--field limit, is discussed and compared with numerical results. An outline of a $1/N$-expansion is given.
4pp., 1 ps figure as one uuencoded ps file
4pp., 1 ps figure as one uuencoded ps file