DIVERGENCE OF THE LOCALIZATION LENGTH IN QUANTUM HALL SYSTEMS

The localization properties of a two-dimensional disordered electron gas in a strong external magnetic field are studied. The impurities are considered to be located on a square lattice with random amplitudes. The concentration of these impurities is low, i.e., the average distance between the impurities exceeds the magnetic length. For short-ranged impurity potentials we analytically obtain an exponent $\nu=2/3$ for the divergence of the localization length at the lowest Landau level. The density of states is also calculated.