Weak Field Phase Diagram for an Integer Quantum Hall Liquid

We investigate the transition of a two-dimensional electron gas from the regime of the quantum Hall effect to the regime of weak magnetic fields for a tight-binding model. Unlike previous work, we find the following: (1) the linear field dependence of the extended-state energies is not affected by disorder, although the total density of states below each level of extended states increases with disorder strength; (2) for each Landau band and disorder strength there exists a critical field $B_c$ below which the extended level disappears, with $B_c$ smaller for lower Landau bands. We show how the experimental findings of level flotation and direct transition from high Landau level states to the Anderson insulating phase may be explained in light of our results.