  We have performed large-scale Monte Carlo simulations on a model describing a
(2+1)-dimensional array of dissipative Josephson junctions. We find three
distinct stable quantum phases of the system. The most ordered state features
long-range spatial ordering in the phase $\theta$ of the superconducting order
parameter, but temporal ordering only in spatial gradients $\Delta \theta$, not
in $\theta$. Significantly, the most ordered state therefore does not have 3D
XY ordering. Rather, it features 2D spin waves coexisting with temporally
disordered phases $\theta$. There is also an intermediate phase featuring
quasi-long-range spatial order in $\theta$ coexisting with a gas of instantons
in $\Delta \theta$. We briefly discuss possible experimental signatures of such
a state, which may be viewed as a local metal and a global superconductor. The
most disordered state has phase disorder in all spatio-temporal directions, and
may be characterized as a gas of proliferated vortices coexisting with a gas of
$\Delta \theta$-instantons. The phase transitions between these phases are
discussed. The transition from the most ordered state to the intermediate state
is driven by proliferation of instantons in $\Delta \theta$. The transition
from the intermediate state to the most disordered state is driven by the
proliferation of spatial point vortices in the background of a proliferated
$\Delta \theta$-instanton gas, and constitutes a
Berezinskii-Kosterlitz-Thouless phase transition. The model also features a
direct phase transition from the most ordered state to the most disordered
state, and this transition is neither in the 2D XY nor in the 3D XY
universality class. It comes about via a simultaneous proliferation of point
vortices in two spatial dimensions and $\Delta \theta$-instantons, with a
complicated interplay between them.
