Abstract
We re-examine the non-linear σ-model lagrangian for the soft modes of non-interacting electrons in a disordered system in a weak magnetic field, close to two dimensions. The magnetic field is shown to induce two scaling terms in the low-energy lagrangian. The crossover exponents are computed by using a Wilson-Polyakov non-linear renormalization group. The largest one agrees to lowest order with the exponent expected from naive scaling arguments.
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