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Published on: March 19, 2016
Study and characterization of interfaces in a two-dimensional generalized voter model
Clelia M Bordogna1, Ezequiel V Albano
1Facultad de Ingeniería, UNLP, Calle 115 Esquina 50, (1900) La Plata, Argentina.
Summary
This study uses numerical simulations to analyze interface evolution in a generalized voter model. We characterized three interface types, revealing power-law behavior and insights into interface coarsening dynamics.
Area of Science:
- Statistical Physics
- Complex Systems
- Computational Physics
Background:
- The voter model is a fundamental framework for studying opinion dynamics and phase transitions.
- Understanding interface evolution is crucial in various fields, including materials science and social dynamics.
Purpose of the Study:
- To investigate the time evolution of interfaces in a generalized voter model in two dimensions.
- To characterize different types of interfaces based on their behavior and the presence of surface tension.
- To provide a unified approach for understanding interface coarsening phenomena.
Main Methods:
- Numerical simulations were employed to model the system's time evolution.
- The generalized voter model was used, where opinion change probability depends on neighbors' average opinion.
- Interface width (w) was measured over time to identify power-law dependencies (w ∝ t^δ).
Main Results:
- Three distinct interface types were characterized: ordered-disordered, ordered-ordered without surface tension, and ordered-ordered with surface tension.
- Power-law behavior was observed for interface width, with an exponent δ=1/2 for the first two types.
- A finite-size induced crossover was found for interfaces with surface tension, showing exponents δ=1/4 (early times) and δ=1/2 (longer times).
Conclusions:
- The study offers a unified framework for characterizing diverse interfaces in the generalized voter model.
- The findings provide valuable insights into the mechanisms of interface coarsening, both with and without surface tension.
- This research contributes to a deeper understanding of collective behavior and pattern formation in complex systems.
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