The Order-disorder Transition in Incompressible Polar Active Fluids with an Easy Axis

Dry active matter in an anisotropic medium is of experimental relevance, and the interplay between anisotropy and the dynamics of the active matter remains under-explored. Here, we derive the hydrodynamic equations of a generic dry polar active fluid that preferentially flows along a particular axis induced by the anisotropy of the medium. We then study its critical behavior at the order-disorder transition in which the symmetry between ``forward" and ``back" along the special axis is spontaneously broken. We obtain the critical static and dynamic exponents, mean velocity, and two point correlation functions exactly in three dimensions, and to two-loop level in two dimensions, by mapping our class of systems to the equilibrium Ising model with dipolar interactions.