Noise-Induced Phase Transition

Parameters

Noise intensity σ²0.50 Coupling κ (MF)1.00 N particles200 a (bistable param)1.00

Observables

⟨x⟩ (mean field)—

|⟨x⟩| (order param)—

Variance σ²(x)—

Phase—

Theory

Each particle obeys a SDE with multiplicative noise and mean-field coupling:

dx = [ax−x³+κ(⟨x⟩−x)]dt
+ σ·x·dW

Horsthemke & Lefever (1984): multiplicative noise shifts the effective potential. Above a critical noise level, a disordered (zero-mean) state can become ordered. Noise creates, rather than destroys, order.