Flocking as a second-order phase transition in self-aligning active crystals

TL;DR

This paper develops a microscopic theory for flocking in active crystals, showing it as a second-order phase transition with a Landau-Ginzburg model, supported by simulations and relevant to biological and granular systems.

Contribution

It introduces the first analytical microscopic theory mapping active crystal dynamics to a Landau-Ginzburg model, revealing flocking as a second-order phase transition.

Findings

Quantitative prediction of the transition point.

Identification of a Mexican-hat effective free energy profile.

Flocking behavior characterized as a second-order phase transition.

Abstract

We study a two-dimensional crystal composed of active units governed by self-alignment. This mechanism induces a torque that aligns a particle's orientation with its velocity and leads to a phase transition from a disordered to a flocking crystal. Here, we provide the first microscopic theory that analytically maps the crystal dynamics onto a Landau-Ginzburg model, in which the velocity-dependent effective free energy undergoes a transition from a single-well shape to a Mexican-hat profile. As confirmed by simulations, our theory quantitatively predicts the transition point and characteristic spatial velocity correlations. The continuous change of the order parameter and the diverging behavior of the analytically predicted correlation length imply that flocking in self-aligning active crystals is a second-order phase transition. These findings provide a theoretical foundation for the flocking phenomenon observed experimentally in active granular particles and migrating cells.