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Percolation and coarsening in the bidimensional voter model
Alessandro Tartaglia1, Leticia F Cugliandolo1, Marco Picco1
1Sorbonne Universités, Université Pierre et Marie Curie-Paris VI, Laboratoire de Physique Théorique et Hautes Energies UMR 7589, 4 Place Jussieu, 75252 Paris Cedex 05, France.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|November 14, 2015
Summary
The bidimensional voter model shows two distinct dynamic regimes: critical site percolation and full consensus. Growing lengths exhibit algebraic time dependence with different exponents, differing from curvature-driven coarsening.
Area of Science:
- Statistical Physics
- Complex Systems
Background:
- The voter model is a fundamental tool for studying opinion dynamics.
- Understanding large-scale emergent behavior in systems with interacting agents is crucial.
Purpose of the Study:
- To investigate the dynamic regimes of the bidimensional voter model on a square lattice.
- To analyze the growth dynamics and cluster morphology within this model.
Main Methods:
- Numerical simulations were employed to study the bidimensional voter model.
- Time dependence of growing lengths was calculated.
- Cluster morphology and statistics were analyzed.
Main Results:
- Two distinct dynamic regimes were identified: approach to critical site percolation and approach to full consensus.
- Two growing lengths were found to depend algebraically on time with different exponents.
- Cluster analysis revealed specific morphologies and statistics.
Conclusions:
- The bidimensional voter model exhibits complex dynamics not fully captured by simpler models.
- The observed dynamics differ from those seen in curvature-driven coarsening processes.
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