Network models of quantum percolation and their field-theory representations

Abstract

We obtain the field-theory representations of several network models that are relevant to two-dimensional transport in high magnetic fields. Among them, the simplest one, which is relevant to the plateau transition in the quantum Hall effect, is equivalent to a particular representation of an antiferromagnetic SU(2N) (N→0) spin chain. Since the latter can be mapped onto a θ≠0, U(2N)/U(N)×U(N) σ model, and since recent numerical analyses of the corresponding network give a delocalization transition with ν≊2.3, we conclude that the same exponent is applicable to the σ model.