The static Hall conductivity in the presence of a strong magnetic field and random impurities

Using the supersymmetric formalism of Brézin, Gross, Itzykson, we compute the Hall conductivity of a two-dimensional electron gas, in the presence of a strong magnetic field and impurities, resulting from a very weak static electric field. This conductivity is found to be not quantised, in contrast to what is expected for the conductivity obtained from an electric field, adiabatically switched on.