Voter Model — Interface Density Coarsening (1D)

In the 1D voter model, each site adopts the opinion of a random neighbor at each step. Domains coarsen algebraically in time as interfaces perform random walks and annihilate on meeting. The interface density ρ(t) ~ t⁻¹/² — a hallmark of coarsening dynamics without surface tension.

Controls

System size N: 400 Noise q: 0.00 Speed: 5

Theory

Interface density:

ρ(t) ~ t⁻¹/²

Coarsening exponent

z = 2 (diffusive)

In 1D: consensus

reached in O(N²) steps

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