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 100×100 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.

• Received 10 August 1993

DOI:https://doi.org/10.1103/PhysRevB.49.3340