2-DIMENSIONAL ELECTRON IN A RANDOM MAGNETIC-FIELD

We study the effect of a random magnetic field on the behavior of the density of states in the Harper problem. By complete diagonalization of lattices of 100X100 sites we show the manner in which the Landau subbands disappear with increasing disorder. At maximum disorder zero-counting techniques for lattices with a large number of sites, up to several million, show the density of states becoming flat and with a narrow bandwidth compared to the pure model in zero field. This allows detailed comparison with previous analytical calculations of the Lifshitz tails. The self-retracing-path approximation gives a good account of the results, except for the tail.