Voter Model — Opinion Dynamics & Coarsening

Each agent copies a random neighbor each step. Clusters grow as √t (2D), interfaces decay, and consensus emerges. In noisy voter model, noise prevents full ordering.

Grid size N 80

Initial density p₀ 0.50

Noise rate ε 0.00 ε>0: noisy voter (no consensus)

Speed 5

Time: 0 sweeps
Magnetization: —
Interface density: —
Consensus: No

Voter model: in 1D, τ~N²; in 2D, τ~N²/ln(N); in 3D, active coexistence survives. Interface density ρ ~ 1/√t (Clifford-Sudbury 1973).

Noisy voter (ε>0): adds spontaneous flips → steady state with fluctuations, no consensus.

Spin lattice: blue=+1, red=−1

Magnetization m(t)

Interface density ρ(t) — expect ~ 1/√t

Cluster size distribution P(s) — should be power law near criticality