Self-propelled particles align with their neighbors. Below a noise threshold, the flock spontaneously orders — a non-equilibrium phase transition unique to active matter (violates detailed balance).
Vicsek model (1995): each particle moves at speed v and aligns heading with neighbors within radius r, plus noise η. First-order phase transition at η_c: disordered → polar-ordered flock. Defies Mermin-Wagner (active matter is non-equilibrium and breaks continuous symmetry in 2D).