Critical phenomena in compressible polar active fluids: Dynamical and functional renormalization group studies

Active matter is not only relevant to living matter and diverse nonequilibrium systems, but also constitutes a fertile ground for novel physics. Indeed, dynamic renormalization group (DRG) analyses have uncovered many new universality classes (UCs) in polar active fluids (PAFs)-an archetype of active matter systems. However, due to the inherent technical difficulties in the DRG methodology, almost all previous studies have been restricted to polar active fluids in the incompressible or infinitely compressible (i.e., Malthusian) limits, and, when the e expansion was used in conjunction, to the one-loop level. Here, we use functional renormalization group (FRG) methods to overcome some of these difficulties and unveil critical behavior in compressible polar active fluids, and calculate the corresponding critical exponents beyond the one-loop level. Specifically, we investigate the multicritical point of compressible PAFs, where the critical order-disorder transition coincides with critical phase separation. We first study the critical phenomenon using a DRG analysis and find that it is insufficient since two-loop effects are important to obtain a nontrivial correction to the scaling exponents. We then remedy this defect by using a FRG analysis. We find three universality classes and obtain their critical exponents, which we then use to show that at least two of these universality classes are out of equilibrium because they violate the fluctuation-dissipation relation.

Automated summary

Active matter is a fertile ground for novel physics, and dynamic renormalization group (DRG) analysis has revealed many new universality classes in polar active fluids (PAFs). However, previous studies have been limited due to technical difficulties, and only explored compressible PAFs at the one-loop level. In this study, we use functional renormalization group (FRG) methods to overcome these limitations and uncover critical behavior in compressible PAFs, calculating critical exponents beyond the one-loop level. We find three universality classes, and show that at least two of these classes violate the fluctuation-dissipation relation, indicating they are out of equilibrium.