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Coarsening dynamics for spiral and disordered waves in active Potts models.
1University of Tokyo, Institute for Solid State Physics, Kashiwa, Chiba 277-8581, Japan.
Physical Review. E
|June 19, 2026
Summary
Active Potts models exhibit wave-like domain growth, following the Lifshitz-Allen-Cahn law. Higher state counts (q) and disordered waves show increased transient growth rates before saturation.
Area of Science:
- Statistical mechanics
- Complex systems dynamics
- Phase transitions
Background:
- Active Potts models simulate systems with interacting components and dynamic behavior.
- Understanding domain growth is crucial for materials science and pattern formation.
- Cyclic symmetry introduces unique dynamics in these models.
Purpose of the Study:
- To investigate the domain-growth dynamics in q-state active Potts models (q=3-8) under cyclic symmetry.
- To analyze coarsening dynamics from random states to emergent moving-domain waves.
- To determine the influence of model parameters and lattice types on growth behavior.
Main Methods:
- Monte Carlo simulations were employed on square and hexagonal lattices.
- Active cyclic flipping of states was implemented to induce wave formation.
- Correlation length and mean cluster size were tracked over time.
Main Results:
- Domain growth followed the Lifshitz-Allen-Cahn (LAC) law (∝t^{1/2}) in intermediate times, with saturation at characteristic wavelengths.
- A transient increase in the coarsening exponent was observed before saturation.
- Higher q values and disordered waves showed greater transient increases; lattice type and update scheme had no impact.
Conclusions:
- Emergent finite-length waves characterize the long-term dynamics of active Potts models under cyclic symmetry.
- The observed transient growth dynamics are a significant feature of the coarsening process.
- The fundamental growth laws are robust across different lattice structures and update rules.
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