Replica study of a glass transition in disordered superconducting films

We consider a disordered superconducting film in a magnetic field close to the upper critical field. Assuming that the phase transition to the glassy superconducting state exists and that it is second order, we show that it is exactly described by a zero-dimensional replica model having the same form as one that describes 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 smoother 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, its part emerging due to the phase transition is shown to be paramagnetic, which agrees with experiments on Nb superconducting films. (orig.)