Strongly Screened Vortex Lattice Model with Disorder

The three dimensional XY model with quenched random disorder and finite screening is studied. We argue that the system scales to model with λ≃0≃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≃+1.0 for weak disorder. For low magnetic field and weak disorder, there is also a superconducting phase with θ≃+1.0 which we conjecture is a Bragg glass. For larger disorder or applied field, there is a non superconducting phase with θ≃−1.0. We estimate the critical external field whose value is consistent with experiment