Spin-Orbit Scattering and Spin-Splitting in the Quantum Hall Effect

We study dynamics of electrons in a magnetic field using a network model with two channels per link with random mixing, while the intrachannel potential is periodic (nonrandom); the channels represent two-spin states. We consider channel mixing as function of the energy separation Δ of the two extended states. We show that for Δ < 0.5 the system has only one extended state, and a localization length diverges approaching it with a nontrivial critical exponent ν ≈︂ 1.1, whereas for larger Δ a transition to a typical quantum Hall behavior with two extended states occurs, and the critical exponent becomes ν ≈︂ 2.5.