  A lattice model of three-state stochastic phase-coupled oscillators has been
shown by Wood et al (2006 Phys. Rev. Lett. 96 145701) to exhibit a phase
transition at a critical value of the coupling parameter, leading to stable
global oscillations. We show that, in the complete graph version of the model,
upon further increase in the coupling, the average frequency of collective
oscillations decreases until an infinite-period (IP) phase transition occurs,
at which point collective oscillations cease. Above this second critical point,
a macroscopic fraction of the oscillators spend most of the time in one of the
three states, yielding a prototypical nonequilibrium example (without an
equilibrium counterpart) in which discrete rotational (C_3) symmetry is
spontaneously broken, in the absence of any absorbing state. Simulation results
and nucleation arguments strongly suggest that the IP phase transition does not
occur on finite-dimensional lattices with short-range interactions.
