An infinite-period phase transition versus nucleation in a stochastic model of collectiveoscillations

Abstract

A lattice model of three-state stochastic phase-coupled oscillators has been shown by Woodet al (2006 Phys. Rev. Lett. 96 145701) to exhibit a phase transition at a critical value ofthe coupling parameter, leading to stable global oscillations. We show that, inthe 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. Abovethis second critical point, a macroscopic fraction of the oscillators spend mostof the time in one of the three states, yielding a prototypical nonequilibriumexample (without an equilibrium counterpart) in which discrete rotational (C3) symmetry is spontaneously broken, in the absence of any absorbing state. Simulationresults and nucleation arguments strongly suggest that the IP phase transition does notoccur on finite-dimensional lattices with short-range interactions.