UNIVERSAL MULTIFRACTALITY IN QUANTUM HALL SYSTEMS WITH LONG-RANGE DISORDER POTENTIAL

We investigate numerically the localization-delocalization transition in quantum Hall systems with long-range disorder potential with respect to multifractal properties. Wave functions at the transition energy are obtained within the framework of the generalized Chalker-Coddington network model. We determine the critical exponent a(0) characterizing the scaling behaviour of the local order parameter for systems with potential correlation length d up to 12 magnetic lengths l. Our results show that a(0) does not depend on the ratio d/l. With increasing d/l, effects due to classical percolation only cause an increase of the microscopic length scale, whereas the critical behaviour on larger scales remains unchanged. This proves that systems with long-range disorder belong to the same universality class as those with short-range disorder.