Noisy Majority-Vote Model

Opinion dynamics with noise: spins flip against local majority with probability q, yielding a continuous order-disorder phase transition

Parameters

Magnetization |m|
Step
0
+1 fraction
Phase
Majority-Vote Model (Oliveira 1992)
P(flip | minority) = 1 - q
P(flip | majority) = q
P(flip | tie) = 1/2

Order param: m = ⟨|∑σᵢ/N|⟩
Critical noise qc ≈ 0.075 (2D square)
Same universality class as 2D Ising
(β=1/8, γ=7/4, ν=1)
Unlike the Ising model driven by temperature, the majority-vote model uses a noise parameter q. Despite having no Hamiltonian, it belongs to the same universality class as the 2D Ising model — a remarkable example of universality in non-equilibrium systems.