Active Matter — Vicsek Flocking & Density Waves
Self-propelled particles: noise-driven order-disorder transition
Order parameter φ = 0.00 | Phase: disordered
Vicsek model (1995): each particle moves at constant speed v₀, aligning its direction with neighbors within radius r, plus noise η.
At low noise: long-range polar order (φ→1) — a flock emerges. At high noise: disordered gas (φ→0).
This non-equilibrium transition has no equilibrium analog — Mermin-Wagner forbids LRO in 2D equilibrium, but activity breaks detailed balance.
Giant number fluctuations (ΔN ~ N^0.8) are a hallmark of the ordered phase.