Enhancement of Superconductivity due to Magnetic Fields in Composite D-wave Superconductors

We study the response of composite D-wave superconductors to weak magnetic fields, at temperatures much lower than the bulk critical temperature. Such systems are formed by superconducting droplets, embedded into a normal metal host in a random fashion. Such system can be modeled as a network of XY spins, with strongly disordered Josephson couplings. We show that the application of a weak magnetic field enhances the superconducting fraction of the system in a non analytic way, as well as the critical temperature. This has to be compared with homogeneous superconductors, whose superconducting properties are always reduced by magnetic fields.