Study of the critical properties of the Quantum Hall Fluid in the framework of a dual statistical model

Study of the critical properties of the Quantum Hall Fluid in the framework of a dual statistical model. Abstract By using Renormalization Group methods we analyze the outcome of a recent proposal of describing the Quantum Hall fluid in terms of a dual plasma which embodies dyons as effective degrees of freedom. As a consequence the physical interpretation of the two parameters of the model as the longitudinal and the Hall conductances is made clear. Parameters' scaling roperties allow for the determination of the critical index for the localization length after a mapping of our statistical model onto a classical percolation model. The universality of the critical properties, supported by recent experiments, is a consequence of the infinite discrete symmetry of the model SL(2, Z) (generalized duality), as noticed in a previous paper.