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We study the localization properties of two-dimensional electrons in a weakperpendicular magnetic field. For this purpose we construct weakly chiralnetwork models on the square and triangular lattices, by separating in spacethe regions with phase action of magnetic field, where it affects interferencein course of disorder scattering, and the regions with orbital action ofmagnetic field, where it bends electron trajectories. In our models, thedisorder mixes counter-propagating channels on the links, while scattering atthe nodes describes the bending of electron trajectories. By introducing astrong spread in the scattering strengths on the links, we eliminate theinterference and reduce the electron propagation over a network to apercolation problem. In this limit we establish the form of the disorder vs.magnetic field phase diagram, which is in agreement with levitation scenario:energy separating the Anderson and quantum Hall insulating phases floats up toinfinity upon decreasing magnetic field. From numerical study we conclude thatthe positions of the weak-field quantum Hall transitions on the phase diagramare very close to our percolation results. We checked that, in accord with thePruisken's theory, presence or absence of time reversal symmetry has no effecton the line of delocalization transitions.

Weakly chiral networks and 2D delocalized states in a weak magnetic field