Phase transitions in the two-dimensional random gauge XY model

The two-dimensional random gauge XY model, where the quenched random variables are magnetic bond angles uniformly distributed within $[-r\pi ,r\pi ](0\mathrm{}<~r<~1),$ is studied via Monte Carlo simulations. We investigate the phase diagram in the plane of the temperature T and the disorder strength r and infer, in contrast to a prevailing conclusion in many earlier studies, that the system is superconducting at any disorder strength r for sufficiently low T. It is also argued that the superconducting to normal transition has different nature at weak disorder and strong disorder: termed Kosterlitz-Thouless (KT) type and non-KT type, respectively. The results are compared to earlier works.