The low noise phase of a 2d active nematic

TL;DR

This paper investigates the behavior of a 2D active nematic system, revealing that noise induces quasi-long-range order, giant number fluctuations persist with finite-size effects, and activity influences density correlations without causing phase separation.

Contribution

It provides a systematic hydrodynamic analysis of 2D active nematics, showing activity is dangerously irrelevant and detailing the nature of fluctuations and correlations.

Findings

Quasi-long-range orientational order persists beyond a crossover scale.

Giant number fluctuations remain with strong finite-size effects.

Active currents lead to power-law density correlations, preventing phase separation.

Abstract

We consider a collection of self-driven apolar particles on a substrate that organize into an active nematic phase at sufficiently high density or low noise. Using the dynamical renormalization group, we systematically study the 2d fluctuating ordered phase in a coarse-grained hydrodynamic description involving both the nematic director and the conserved density field. In the presence of noise, we show that the system always displays only quasi-long ranged orientational order beyond a crossover scale. A careful analysis of the nonlinearities permitted by symmetry reveals that activity is dangerously irrelevant over the linearized description, allowing giant number fluctuations to persist though now with strong finite-size effects and a non-universal scaling exponent. Nonlinear effects from the active currents lead to power law correlations in the density field thereby preventing macroscopic phase separation in the thermodynamic limit.