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We consider a recently proposed network model of the integer quantum Hall(IQH) effect in a weak magnetic field. Using a supersymmetry approach, wereformulate the network model in terms of a superspin ladder. A subsequentanalysis of the superspin ladder and the corresponding supersymmetric nonlinearsigma model allows to establish the phase diagram of the network model, and theform of the critical line of the weak-field IQH transition. Our results confirmthe universality of the IQH transition, which is described by the same sigmamodel in strong and weak magnetic fields. We apply the suspersymmetry method toseveral related network models that were introduced in the literature todescribe the quantum Hall effect in graphene, the spin-degenerate Landaulevels, and localization of electrons in a random magnetic field.

Supersymmetry approach to delocalization transitions in a network model of the weak field quantum Hall effect and related models