  We consider a recently proposed network model of the integer quantum Hall
(IQH) effect in a weak magnetic field. Using a supersymmetry approach, we
reformulate the network model in terms of a superspin ladder. A subsequent
analysis of the superspin ladder and the corresponding supersymmetric nonlinear
sigma model allows to establish the phase diagram of the network model, and the
form of the critical line of the weak-field IQH transition. Our results confirm
the universality of the IQH transition, which is described by the same sigma
model in strong and weak magnetic fields. We apply the suspersymmetry method to
several related network models that were introduced in the literature to
describe the quantum Hall effect in graphene, the spin-degenerate Landau
levels, and localization of electrons in a random magnetic field.
