CLASSICAL ANALOGS TO THE CHALKER-CODDINGTON MODEL

A description is given of a classical analogs to the Chalker-Coddingto n model, i.e. of a lattice model of the integer quantum Hall effect, w hich has recently been used to investigate intensively mesoscopic cond uctance fluctuations at the plateau transition. It is shown that the c orresponding classical problem is current percolation through bonds fo rming a two-dimensional percolation-cluster hull. It is also shown tha t, in contrast to standard percolative problems, the scaling relations for conductance, as also the conductance distribution function for fi nite samples, contains only the critical correlation-length exponent i n the problem under study. It is known that such relations developed f or the integer quantum-Hall effect likewise contain only the critical correlation-length exponent. It is finally concluded that this essenti al feature of the quantum Hall effect is determined not so much by its quantum nature as by the geometry of the problem. (C) 1998 American I nstitute of Physics.