N coupled phase oscillators with disorder. The Kuramoto model shows a continuous phase transition from incoherence to synchrony at coupling K=Kc=2/(πg(0)) where g is the frequency distribution.
dθᵢ/dt = ωᵢ + (K/N)Σⱼsin(θⱼ-θᵢ). Order parameter r=|N⁻¹Σe^{iθⱼ}|∈[0,1]. Critical coupling Kc=2/πg(0)=2σ√(2π)/π=2σ√(2/π) for Gaussian g. For K>Kc: r≈√(1-Kc/K) near transition (β=1/2 mean-field exponent). Discovered by Kuramoto 1975; the model is exactly solvable via the Ott-Antonsen ansatz (2008).