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Effect of initial conditions on Glauber dynamics in complex networks
Makoto Uchida1, Susumu Shirayama
1Research into Artifacts, Center for Engineering (RACE), University of Tokyo, 5-1-5 Kashiwanoha, Kashiwa, Chiba 277-8568, Japan. uchida@race.u-tokyo.ac.jp
Summary
Initial spin configurations significantly impact spin dynamics in complex networks. The starting state influences outcomes as much as network structure, revealing complex behaviors and critical points.
Area of Science:
- Statistical Physics
- Network Science
- Complex Systems
Background:
- Glauber spin dynamics are crucial for understanding emergent behaviors in complex systems.
- Network structure and initial conditions are known factors influencing system dynamics.
Purpose of the Study:
- To investigate the effect of initial spin configurations on zero-temperature Glauber spin dynamics.
- To explore how centrality measures as initial spin conditions affect system behavior in complex networks.
Main Methods:
- Simulations of zero-temperature Glauber spin dynamics on complex networks.
- Analysis of initial spin configurations based on vertex centrality measures.
- Examination of the relationship between initial and final fractions of positive spins.
Main Results:
- Nontrivial diffusive behaviors were observed, influenced by initial spin configurations.
- Functional relationships between initial and final spin fractions exhibited critical points.
- The majority spin in the initial state did not consistently dominate the final state.
- Spin dynamics phenomena varied based on initial conditions, even for identical networks.
Conclusions:
- Initial spin configurations exert a strong influence on spin dynamics, comparable to network structure.
- The choice of initial conditions is critical for predicting the emergent behavior of complex networks.
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