  The two-dimensional random gauge \xy model, where the quenched random
variables are magnetic bond angles uniformly distributed within $[-r\pi, r\pi]$
($0 \leq r \leq 1$), 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.
