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In active matter systems, non-Gaussian, exact scaling exponents have beenclaimed in a range of systems using perturbative renormalization group (RG)methods. This is unusual compared to equilibrium systems where non-Gaussianexponents can typically only be approximated, even using the exact (orfunctional/nonperturbative) renormalization group (ERG). Here, we perform anERG analysis on the ordered phase of incompressible polar active fluids andfind that the exact non-Gaussian exponents obtained previously using aperturbative RG method remain valid even in this nonperturbative setting.Furthermore, our ERG analysis elucidates the RG flow of this system and enablesus to identify an active Goldstone regime with nontrivial, long-ranged scalingbehavior for parallel and longitudinal fluctuations.

Can exact scaling exponents be obtained using the renormalization group? Affirmative evidence from incompressible polar active fluids