SEALING BEHAVIOR AND UNIVERSALITY NEAR THE QUANTUM HALL TRANSITION

A two-dimensional lattice system of noninteracting electrons in a homo geneous magnetic field with half a flux quantum per plaquette and a ra ndom potential is considered. For the large-scale behavior a supersymm et ric theory with collective fields is constructed and studied within saddle-point approximation and fluctuations. The modelis characterize d by a broken supersymmetry indicating that only the fermion collectiv e field becomes delocaIized whereas the boson field is exponentially l ocalized. Power counting for the Auctuation terms suggests that the in teractions between delocalized Auctuations are irrelevant. Several qua siscaling regimes, separated by large crossover lengths, are found wit h effective exponents v for the localization length xi(l). In the asym ptotic regime there is v = 1/2 in agreement with an earlier calculatio n of Affleck and one by Ludwig et al. for a finite density of states. The effective exponent, relevant for physical system, is v = 1 where t he coefficient of xi(l) is growing with randomness. This is in agreeme nt with recent high-precision measurements on Si metal-oxide-semicondu ctor field-effect transistor, and AlxGa1-xAs/GaAs samples.