In this paper we study a spatially periodic stochastic system with infinite globally coupled oscillators driven by a constant force F. With two typical models we show that when $F=0\mathrm{}$ there is a nonequilibrium transition between the state with zero mean field $\mathrm{}(s=0\mathrm{})\mathrm{}$ and the state with nonzero mean field $\left(s\ne 0\right).$ For model I, the transition is not a phase transition, while for the model II it is (second order). In addition, we find that for coupled oscillators driven only by additive noises, when $F=0\mathrm{}$ a transport may emerge if the nonzero mean field breaks the symmetry of the systems. With varying F a continuous or discontinuous transition between state $s>\mathrm{}0\mathrm{}$ and state $s<\mathrm{}0\mathrm{}$ will appear. The mean field or current sometimes exhibits hysteresis as a function of F.

• Received 9 January 2001

DOI:https://doi.org/10.1103/PhysRevE.64.011106