Percolation and coarsening in the bidimensional voter model

TL;DR

This paper investigates the dynamics of the bidimensional voter model, revealing two distinct regimes: initial approach to critical percolation and eventual consensus, with algebraic growth of characteristic lengths and analysis of cluster morphology.

Contribution

It provides a detailed numerical analysis of the voter model's evolution, identifying two dynamic regimes and comparing cluster statistics to curvature-driven coarsening.

Findings

Two dynamic regimes identified: percolation and consensus

Both characteristic lengths grow algebraically with different exponents

Cluster morphology analyzed and compared to coarsening processes

Abstract

We study the bidimensional voter model on a square lattice with numerical simulations. We demonstrate that the evolution takes place in two distinct dynamic regimes; a first approach towards critical site percolation and a further approach towards full consensus. We calculate the time-dependence of the two growing lengths finding that they are both algebraic though with different exponents (apart from possible logarithmic corrections). We analyse the morphology and statistics of clusters of voters with the same opinion. We compare these results to the ones for curvature driven two-dimensional coarsening.