  Synchronization of stochastic phase-coupled oscillators is known to occur but
difficult to characterize because sufficiently complete analytic work is not
yet within our reach, and thorough numerical description usually defies all
resources. We present a discrete model that is sufficiently simple to be
characterized in meaningful detail. In the mean field limit, the model exhibits
a supercritical Hopf bifurcation and global oscillatory behavior as coupling
crosses a critical value. When coupling between units is strictly local, the
model undergoes a continuous phase transition which we characterize numerically
using finite-size scaling analysis. In particular, we explicitly rule out
multistability and show that that the onset of global synchrony is marked by
signatures of the XY universality class. Our numerical results cover dimensions
d=2, 3, 4, and 5 and lead to the appropriate XY classical exponents \beta and
\nu, a lower critical dimension d_{lc} = 2, and an upper critical dimension
d_{uc}=4.
