Geometrical exponents in the integer quantum Hall effect

We point out that the extended Chalker-Coddington model in the ''classical'' limit, i.e. the limit of large disorder, shows crossover to the so-called ''smart kinetic walks''. The reason why this limit has previously been identified with ordinary percolation is, presumably, that the localization length exponents nu coincide for the two problems. Other exponents, like the fractal dimension D, differ. This gives an opportunity to test the consistency of the semiclassical picture of the localization-delocalization transitions in the integer quantum Hall effect. We calculate numerically, using the extended Chalker-Coddington model, two exponents tau and D that characterize critical properties of the geometry of the wave function at these transitions. We find that the exponents, within our precision, are equal to those of two-dimensional percolation, as predicted by the semiclassical picture.