On the implications of discrete symmetries for the β-function of quantum Hall systems

We argue that the large discrete-symmetry group of quantum Hall systems is insufficient in itself to determine the complete beta-function for the scaling of the conductivities, sigma(xx) and sigma(xy). We illustrate this point by showing that a recent ansatz for this function is one of a many-parameter family. A clean prediction for the delocalization exponents for these systems therefore requires the specification of more information, such as past proposals that the beta-function is either holomorphic or quasi-holomorphic in the variable z= (h/e(2))(sigma(xy) + i sigma(xx)). (C) 199 Published by Elsevier Science B.V. All rights reserved.