  We study the localization properties of two-dimensional electrons in a weak
perpendicular magnetic field. For this purpose we construct weakly chiral
network models on the square and triangular lattices, by separating in space
the regions with phase action of magnetic field, where it affects interference
in course of disorder scattering, and the regions with orbital action of
magnetic field, where it bends electron trajectories. In our models, the
disorder mixes counter-propagating channels on the links, while scattering at
the nodes describes the bending of electron trajectories. By introducing a
strong spread in the scattering strengths on the links, we eliminate the
interference and reduce the electron propagation over a network to a
percolation 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 to
infinity upon decreasing magnetic field. From numerical study we conclude that
the positions of the weak-field quantum Hall transitions on the phase diagram
are very close to our percolation results. We checked that, in accord with the
Pruisken's theory, presence or absence of time reversal symmetry has no effect
on the line of delocalization transitions.

Mesoscale and Nanoscale Physics