Vicsek Model — Flocking Order-Disorder Transition

The Vicsek model is a minimal model of collective motion where self-propelled particles align with neighbors subject to angular noise. Above a critical noise η_c the system disorders (φ→0); below it, a polar ordered phase emerges (φ→1) with spontaneously broken rotational symmetry. This is a genuine non-equilibrium phase transition with long-range order in 2D, defying Mermin-Wagner.

Order φ = 0 | —