0.32
30
5
100
Order parameter φ
0.00
|⟨e^{iθ}⟩|
1.0 = fully aligned
0.0 = random
0.0 = random
Vicsek model (1995): particles move at fixed speed, align direction with neighbors within radius r, plus noise η. At low noise/high density: ordered flocking. At high noise: disordered gas. Second-order-like phase transition at η_c.