  The two dimensional surface of an integer quantum hall multilayer is mapped
onto a Heisenberg spin-chain with ferromagnetic coupling. Using this mapping it
is shown non-perturbatively that the surface states constitute a very
anisotropic metal in the infinite size limit. For multilayers of finite size,
two diffusive mesoscopic regimes are identified and the conductance
fluctuations are calculated perturbatively for both. The Heisenberg spin-chain
representation is used to study the directed wave problem and the exact result
is obtained that the mean-square deflection of a directed wave grows as the
square root of the propagation of the distance.
