Glassy vortex state in a two-dimensional disordered XY model

The two-dimensional XY model with random phase shifts on bonds is studied. The analysis is based on a renormalization group for the replicated system. The model is shown to have an ordered phase with quasi-long-range order. This ordered phase consists of a glasslike region at lower temperatures and of a nonglassy region at higher temperatures. The transition from the disordered phase into the ordered phase is not reentrant and is of a new universality class at zero temperature. In contrast to previous approaches the disorder strength is found to be renormalized to larger values. Several correlation functions are calculated for the ordered phase. They allow one to identify not only the transition into the glassy phase but also an additional crossover line, where the disconnected vortex correlation changes its behavior on large scales nonanalytically. The renormalization group approach yields the glassy features without a breaking of replica symmetry.