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

TL;DR

This paper provides evidence that exact non-Gaussian scaling exponents in active matter can be obtained through the nonperturbative ERG method, confirming previous perturbative RG results for incompressible polar active fluids.

Contribution

The study demonstrates that perturbative RG exponents remain valid in a nonperturbative ERG framework for active fluids, revealing a long-range Goldstone regime.

Findings

Exact non-Gaussian exponents confirmed by ERG analysis.

Identification of a long-ranged Goldstone regime.

Validation of perturbative RG results in a nonperturbative setting.

Abstract

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