From Phase to Micro-Phase Separation in Flocking Models: The Essential Role of Non-Equilibrium Fluctuations

TL;DR

This paper reveals that non-equilibrium fluctuations are crucial in flocking models, leading to microphase separation and smectic band patterns, contrasting with traditional deterministic predictions.

Contribution

It demonstrates that fluctuations fundamentally alter the phase behavior in flocking models, explaining the emergence of microphase separation and pattern formation.

Findings

Flocking transition resembles a liquid-gas transition.

Microphase separation results in smectic traveling bands.

Fluctuations are essential for pattern selection.

Abstract

We show that the flocking transition in the Vicsek model is best understood as a liquid-gas transition, rather than an order-disorder one. The full phase separation observed in flocking models with Z2 rotational symmetry is, however, replaced by a microphase separation leading to a smectic arrangement of traveling ordered bands. Remarkably, continuous deterministic descriptions do not account for this difference, which is only recovered at the fluctuating hydrodynamics level. Scalar and vectorial order parameters indeed produce different types of number fluctuations, which we show to be essential in selecting the inhomogeneous patterns. This highlights an unexpected role of fluctuations in the selection of flock shapes.