Hall Conductivity in the presence of repulsive magnetic impurities

The Hall conductivity of disordered magnetic systems consisting of hard-core point vortices randomly dropped on the plane with a Poissonian distribution, has a behavior analogous to the one observed experimentally by R.~J.~Haug, R.~R.~Gerhardts, K.~v.~Klitzling and K.~Ploog, with repulsive scatterers \cite {1}. We also argue that models of homogeneous magnetic field with disordered potential, have necessarily vanishing Hall conductivities when their Hilbert space is restricted to a given Landau level subspace.