Phase Transitions in the Two-Dimensional Random Gauge XY Model

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The two-dimensional random gauge model, where the quenched random variables are magnetic bond angles uniformly distributed within [-rπ, rπ] (0 ≤ 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.