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Freezing in random graph ferromagnets
1Institute for Theoretical Physics, Chalmers University of Technology and Göteborg University, SE-412 96 Gothenburg, Sweden. tfkps@fy.chalmers.se
Summary
We studied energy relaxation in ferromagnetic models on random graphs. Unexpected power law relaxation and freezing to metastable states were found due to dynamic frustration, impacting complex system models.
Area of Science:
- Statistical mechanics
- Complex systems modeling
Background:
- Ferromagnetic Ising and Potts models are fundamental in statistical mechanics.
- Understanding energy relaxation dynamics is crucial for complex systems.
Purpose of the Study:
- To investigate energy relaxation in ferromagnetic Ising and Potts models on random graphs.
- To identify conditions leading to deviations from standard exponential decay.
Main Methods:
- T=0 Monte Carlo simulations
- Simulated annealing simulations
- Analysis of energy relaxation on random graphs with varying connectivities.
Main Results:
- Observed power law relaxation and freezing to metastable states for specific graph connectivities.
- Identified dynamic frustration as the cause of freezing, persisting even with simulated annealing.
- Demonstrated that freezing is inherent to local search dynamics in Monte Carlo methods.
Conclusions:
- Dynamic frustration in random graphs can lead to non-exponential energy relaxation and system freezing.
- These findings have implications for agent-based complex system models relying on similar dynamics.