  We consider 3D active plane rotators, where the interaction between the spins
is of XY-type and where each spin is driven to rotate. For the clock-model,
when the spins take N\gg1 possible values, we conjecture that there are two
low-temperature regimes. At very low temperatures and for small enough drift
the phase diagram is a small perturbation of the equilibrium case. At larger
temperatures the massless modes appear and the spins start to rotate
synchronously for arbitrary small drift. For the driven XY-model we prove that
there is essentially a unique translation-invariant and stationary distribution
despite the fact that the dynamics is not ergodic.
