Phase separation in ordered polar active fluids: A completely different universality class from that of equilibrium...

It has recently been shown that large collections of self-propelled entities (a.k.a. "flocks" or, more technically, polar-ordered active fluids), all spontaneously moving in the same direction, can undergo phase separation in the presence of sufficiently strong attractive interactions (which can be caused by, e.g., autochemotaxis). At this transition, the system spontaneously separates into a high-density band and a low-density band, moving parallel to each other, and to the direction of mean flock motion, at different speeds. We show here that phase separation in ordered polar active fluids belongs to a new universality class, completely different from that of phase separation in equilibrium fluids. The upper critical dimension for this transition is d_{c}=5, in contrast to the well-known d_{c}=4 of equilibrium phase separation. With a dynamical renormalization group analysis, we obtain the large-distance, long-time scaling laws of the velocity and density fluctuations, which are characterized by universal critical correlation length and order parameter exponents ν_{⊥}, ν_{∥}, and β, respectively. We calculate these to O(ε) in a d=5-ε expansion.