Chalker-Coddington network model and its applications to various quantum Hall systems
We start by detailed description of the original Cahlker Coddington network model and briefly discuss its various generalizations. We then study a physical system consisting of noninteracting quasiparticles in disordered superconductors that have neither time-reversal nor spin-rotation invariance. This system belongs to class D within the recent classification scheme of random matrix ensembles, and its phase diagram contains three different phases: metallic and two distinct localized phases with different quantized thermal Hall conductances. We find that critical exponents describing different transitions (insulator-to-insulator and insulator-to-metal) are identical within the error of numerical calculations. Finally, we discuss localization-delocalization transition in quantum Hall systems with a random field of nuclear spins acting on two-dimensional electron spins via hyperfine contact Fermi interaction. 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 percolations.