Vicsek Model

Vicsek 1995: Each particle moves with speed v, aligning its heading to the average of neighbors within radius R, plus noise η. At low η: ordered flock (φ→1). At high η: disordered gas (φ→0). A continuous-symmetry-breaking transition (Mermin-Wagner evaded by activity) creates long-range polar order in 2D — forbidden in equilibrium.