Nonexistence of quasi-long-range order in strongly disordered vortex glasses: A rigorous proof

The paper contains a rigorous proof of the absence of quasi-long-range order in the random-field $O(N)$ model for strong disorder in the space of an arbitrary dimensionality. This result implies that quasi-long-range order inherent to the Bragg glass phase of the vortex system in disordered superconductors is absent as the disorder or external magnetic field is strong.