  We explore the phase diagram of interacting spin-$1/2$ systems in the
presence of anisotropic interactions, spontaneous decay and driving. We find a
rich phase diagram featuring a limit cycle phase in which the magnetization
oscillates in time. We analyze the spatio-temporal fluctuations of this limit
cycle phase at the Gaussian level, and show that spatial fluctuations lead to
quasi-long-range limit cycle ordering for dimension $d = 2$. This result can be
interpreted in terms of a spatio-temporal Goldstone mode corresponding to phase
fluctuations of the limit cycle. We also demonstrate that the limit-cycle phase
exhibits an asymmetric power spectrum measurable in fluorescence experiments.
