Classical analogs to the Chalker-Coddington model

Abstract

A description is given of a classical analogs to the Chalker-Coddington model, i.e. of a lattice model of the integer quantum Hall effect, which has recently been used to investigate intensively mesoscopic conductance fluctuations at the plateau transition. It is shown that the corresponding classical problem is current percolation through bonds forming a two-dimensional percolation-cluster hull. It is also shown that, in contrast to standard percolative problems, the scaling relations for conductance, as also the conductance distribution function for finite samples, contains only the critical correlation-length exponent in the problem under study. It is known that such relations developed for the integer quantum-Hall effect likewise contain only the critical correlation-length exponent. It is finally concluded that this essential feature of the quantum Hall effect is determined not so much by its quantum nature as by the geometry of the problem.