CONDUCTANCE AND ITS UNIVERSAL FLUCTUATIONS IN THE DIRECTED NETWORK MODEL AT THE CROSSOVER TO THE QUASI-ONE-DIMENSIONAL REGIME

The directed network model describing chiral edge states on the surfac e of a cylindrical three-dimensional quantum Hall system is known to m ap to a one-dimensional (1D) quantum ferromagnetic spin chain. Using t he spin-wave expansion for this chain, we determine the universal func tions for the crossovers between the two-dimensional chiral metallic a nd 1D metallic regimes in the mean and variance of the conductance alo ng the cylinder, to first nontrivial order.