On the Abrikosov transition in disordered superconducting films

We consider a disordered superconducting film in the magnetic field close to the upper critical field. Assuming that the phase transition to the glassy superconducting state exists and it is of the second order we show that it is exactly described by a zero-dimensional replica model having a form of one describing the phase transition in the SK (Sherrington-Kirkpatrick) spin-glass model. The dependence of the magnetic moment on the external magnetic field is shown to be more smooth than the Abrikosov mean field result for the clean case. While the total magnetic moment of the film close to the phase transition is diamagnetic, the part of it emerging due to the phase transition is paramagnetic, this shows tendency to the paramagnetic Meissner effect.