  We study localization-delocalization transition in quantum Hall systems with
a random field of nuclear spins acting on two-dimensional (2d) electron spins
via hyperfine contact (Fermi) interaction. We use Chalker-Coddington network
model, which corresponds to the projection onto the lowest Landau level. The
inhomogeneous nuclear polarization acts on the electrons as an additional
confining potential, and, therefore, introduces additional parameter $p$ (the
probability to find a polarized nucleus in the vicinity of a saddle point of
random potential) responsible for the change from quantum to classical
behavior. In this manner we obtain two critical exponents corresponding to
quantum and classical percolation. We also study how the 2d extended state
develops into the one-dimensional (1d) critical state.

Mesoscale and Nanoscale Physics