Flocking — Vicsek Alignment & Noise

The Vicsek model (1995): each particle aligns its velocity with neighbors within radius r, plus noise η. A continuous phase transition at critical noise η_c separates ordered (flocking) from disordered phases. Order parameter φ = |⟨e^{iθ}⟩| measures global alignment.

0.50
4.0
0.15
1.0
Order φ
Particles
Phase