Lower critical dimensions of stochastic nonequilibrium ferromagnetic Ising systems

The existence of ordered phases in stochastic Ising dynamical systems with short-range ferromagnetic interactions is discussed with the emphasis on open questions. Various examples of models are presented; some of these do and some others do not undergo positive temperature (i.e., nonzero noise) phase transitions in two and three dimensions. The examples suggest that such equilibrium notions as lower critical dimension may not be uniquely definable for these nonequilibrium systems. The existence of temporally periodic states is also briefly discussed.