2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/20695The two-dimensional random gauge \xy model, where the quenched random variables are magnetic bond angles uniformly distributed within $[-rπ, rπ]$ ($0 \leq r \leq 1$), 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.5 pages in two-column form, 4 figures. To appear in PRBSuperconductivitytext