Novel critical phenomena in compressible polar active fluids: A functional renormalization group approach

Polar active fluids (PAFs) describe the large-scale collective behavior of aligning self-propelling particles, such as birds, fish, or bacteria through hydrodynamic equations of motion. As for passive fluids, one can identify a phase diagram revealing either ordered flocking motion, disordered motion, different states of phase separation, and critical points. Generically, these critical points can be systematically categorized into universality classes (UCs), using renormalization group (RG) methods. Indeed, dynamic RG, together with the perturbative ε-expansion method, has uncovered both novel UCs as well as attributed known UCs to some of the critical points in PAFs in both the incompressible as well as the infinitely compressible limits. Similar studies on the more general compressible PAFs have been hindered by technical difficulties, except for rare cases.

Using functional RG methods, we are able to overcome some of these issues and reveal for the first time critical phenomena in compressible PAFs. Specifically, we show the existence of three novel universality classes around a multicritical region of the PAF phase diagram close to the upper critical dimension d_c=6, two of which are demonstratively out of equilibrium, since their associated scaling behavior violates the fluctuation-dissipation relation equilibrium systems must fulfill.