Flocking as a continuous phase transition in self-aligning active crystals

Area of Science:

• Physics
• Soft Matter Physics
• Statistical Mechanics

Background:

• Active matter systems exhibit emergent behaviors like flocking.
• Self-alignment mechanisms in active units can drive collective motion.
• Understanding phase transitions in these systems is crucial for predicting their dynamics.

Purpose of the Study:

• To develop a microscopic theory for flocking transitions in two-dimensional active crystals.
• To analytically map the crystal dynamics onto a Landau-Ginzburg model.
• To quantitatively predict transition points and velocity correlations.

Main Methods:

• Derivation of a Landau-Ginzburg model from microscopic active crystal dynamics.
• Analytical calculation of velocity-dependent effective free energy.
• Comparison of theoretical predictions with simulation results.

Main Results:

• The theory analytically describes the transition from a disordered to a flocking state.
• A velocity-dependent effective free energy transitions from a single-well to a Mexican-hat profile.
• Quantitative prediction of the transition point and spatial velocity correlations.

Conclusions:

• Flocking in self-aligning active crystals represents a continuous phase transition (BKT type in 2D, second-order in 3D).
• The findings provide a theoretical foundation for experimentally observed flocking in active granular particles and migrating cells.
• This work advances the understanding of collective behavior and phase transitions in active matter.