Abstract
We develop a theory of mesoscopic fluctuations in disordered thin superconducting films in a parallel magnetic field. At zero temperature and sufficiently strong magnetic field the system undergoes a phase transition into a state characterized by a superfluid density which is random in sign. Consequently, in this regime, random supercurrents are spontaneously created in the ground state of the system, and it belongs to the same universality class as the two-dimensional $\mathrm{XY}$ spin glass with a random sign of the exchange interaction.
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