2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/18968The three dimensional XY model with quenched random disorder and finite screening is studied. We argue that the system scales to model with $λ\simeq 0\simeq T$ and the resulting effective model is studied numerically by defect energy scaling. In zero external field we find that there exists a true superconducting phase with a stiffness exponent $θ\simeq +1.0$ for weak disorder. For low magnetic field and weak disorder, there is also a superconducting phase with $θ\simeq +1.0$ which we conjecture is a Bragg glass. For larger disorder or applied field, there is a non superconducting phase with $θ\simeq -1.0$. We estimate the critical external field whose value is consistent with experiment.Extensively revised; 4 pages, 4 figures, Submitted to PRLStatistical MechanicsSuperconductivitytext