  Starting from symmetry considerations, we derive the generic hydrodynamic
equation of non-equilibrium $XY$ spin systems with $N$-atic symmetry under weak
fluctuations. Through a systematic treatment we demonstrate that, in two
dimensions, these systems exhibit two types of scaling behaviours. For $N=1$,
they have long-range order and are described by the flocking phase of dry polar
active fluids. For all other values of $N$, the systems exhibit quasi
long-range order, as in the equilibrium $XY$ model at low temperature.
