Vicsek Model — Flocking & Order-Disorder Transition
Self-propelled particles aligning with neighbors — polar order parameter vs noise strength
Controls
Noise η:
0.3
Density ρ (N/L²):
2.0
Interaction radius r:
1.0
Speed v:
0.3
Reset random
Pause
Order parameter φ:
Vicsek update:
θᵢ(t+1) = ⟨θⱼ⟩_{|rᵢ-rⱼ|<r} + η·ξ
φ = |Σ eⁱθⱼ| / N
Order-disorder transition at η_c(ρ). Above η_c: disordered. Below: flocking band forms (1st-order-like).