SCALING AND UNIVERSALITY IN THE INTEGER QUANTUM HALL-EFFECT

For a model of noninteracting electrons in a disorder potential under quantum Hall conditions the critical behavior near the centers of the two lowest Landau levels and its dependence on the correlation length of the disorder potential are studied. The localization length is calculated numerically for quasi-one-dimensional systems. Finite-size scaling is used to obtain the critical exponent. For the lowest Landau level universal one-parameter scaling independent of the correlation length is found. Universality in the higher Landau levels is established by an argument based on the shape of the potential matrix elements in the limit of large correlation length. In the second lowest Landau-level universality is explicitly demonstrated by comparison of numerical data obtained for a correlation length equal to the magnetic length with those obtained for the lowest Landau level. However, no scaling behavior could be found for short correlation lengths in the first Landau level.