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Three-state cyclic voter model extended with Potts energy
György Szabó1, Attila Szolnoki
1Research Institute for Technical Physics and Materials Science, P. O. Box 49, H-1525 Budapest, Hungary.
Summary
This study extends the voter model to include surface tension effects, revealing distinct pattern formations. Cyclic dominance influences pattern evolution, leading to either loop creation or spiral formation.
Area of Science:
- Statistical Physics
- Complex Systems
Background:
- The voter model simulates opinion dynamics.
- Cyclic dominance introduces non-linear interactions.
- Surface tension influences pattern formation in physical systems.
Purpose of the Study:
- To investigate the impact of surface tension on self-organizing patterns in a cyclically dominated voter model.
- To analyze the geometrical aspects of three-color patterns.
- To understand how surface tension modifies pattern evolution compared to the standard voter model.
Main Methods:
- Extension of the cyclically dominated voter model on a square lattice.
- Incorporation of Potts energy variations during nearest-neighbor invasions.
- Geometrical analysis of emergent three-color patterns.
Main Results:
- In the absence of surface tension (voter model limit), pattern evolution is dominated by loop creation from interfacial roughening.
- In the presence of surface tension, pattern evolution shifts to spiral formation.
- The geometrical parameters of these spirals are dependent on the strength of cyclic dominance.
Conclusions:
- Surface tension significantly alters pattern dynamics in the cyclically dominated voter model.
- The model exhibits distinct self-organizing behaviors under different physical constraints.
- Geometrical analysis provides insights into the mechanisms driving pattern evolution.