Percolation and coarsening in the bidimensional voter model

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.

References in corpus (15)

• Statistical physics of social dynamics
• Recent advances in percolation theory and its applications
• Does a Single Zealot Affect an Infinite Group of Voters ?
• Is the Voter Model a model for voters?
• Decelerating microdynamics can accelerate macrodynamics in the voter model
• Exact results for curvature-driven coarsening in two dimensions
• Domain growth morphology in curvature driven two dimensional coarsening
• Effective surface-tension in the noise-reduced voter model
• Bona Fide Thermodynamic Temperature in Nonequilibrium Kinetic Ising Models
• How soon after a zero-temperature quench is the fate of the Ising model sealed?
• Zero-Temperature Relaxation of Three-Dimensional Ising Ferromagnets
• Zero-Temperature Freezing in Three-Dimensional Kinetic Ising Model
• Geometric properties of two-dimensional coarsening with weak disorder
• Persistence in the two dimensional ferromagnetic Ising model
• Slicing the $3d$ Ising model: critical equilibrium and coarsening dynamics

Cited by in corpus (12)

• Critical percolation in the dynamics of the 2d ferromagnetic Ising model
• Coarsening and percolation in the kinetic $2d$ Ising model with spin exchange updates and the voter model
• Quench dynamics of the three-dimensional U(1) complex field theory: geometric and scaling characterisation of the vortex tangle
• Thermal quenches in the stochastic Gross-Pitaevskii equation: morphology of the vortex network
• Critical percolation in the slow cooling of the bi-dimensional ferromagnetic Ising model
• Coarsening and metastability of the long-range voter model in three dimensions
• Curvature-driven growth and interfacial noise in the voter model with self-induced zealots
• Phase separation and critical percolation in bidimensional spin-exchange models
• Fractal character of the phase ordering kinetics of a diluted ferromagnet
• Critical phenomena in presence of symmetric absorbing states: a microscopic spin model with tunable parameters
• Energy-lowering and constant-energy spin flips: Emergence of the percolating cluster in the kinetic Ising model
• Schrödinger-invariance in the voter model