Pattern of Hall resistance in heterostructures

We try to reproduce the profile of Hall resistance of some experiments in the integer regime for heterostructures. It is shown that the Coulomb interaction cannot explain the odd-filled plateaus' widths. An ad hoc term is added to the energy in order to describe the finite buffer capacity of the bulk. The model is able to reproduce the Hall resistance profile with good approximation. Moreover, it predicts some surprising effects at low carrier density. In this limit Coulomb interaction becomes dominant over the kinetic term; therefore all spins tend to point in the same direction (phase transition) and at some exceptional value of the parameters an inversion in the filling factor occurs (by decreasing the magnetic field the filling factor jumps to the lower value).