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Information exchange dynamics of the two-dimensional XY model
Minsu Kim1, Daun Jeong2, H W Kwon3
1Department of Physics and Astronomy and Center for Theoretical Physics, Seoul National University, Seoul 151-747, Korea and Soil and Terrestrial Environmental Physics (STEP), Institute of Terrestrial Ecosystems (ITES), ETH Zurich, 8092 Zurich, Switzerland.
Information exchange in the two-dimensional XY model shows emergent criticality. Relaxation times grow algebraically with system size, indicating no characteristic time scales in the thermodynamic limit.
Area of Science:
- Statistical Mechanics
- Condensed Matter Physics
Background:
- The two-dimensional XY model is a fundamental model in statistical mechanics.
- Understanding information exchange dynamics is crucial for complex systems.
Purpose of the Study:
- To investigate the information exchange dynamics of the two-dimensional XY model.
- To determine the relationship between system size and relaxation times.
Main Methods:
- Utilizing the entropic sampling algorithm for numerical analysis.
- Combining analytic and numerical results to calculate entropy.
- Exploring time evolution of order parameter and vortex number.
Main Results:
- Entropy calculated across the full energy range for various system sizes.
- Relaxation times exhibit algebraic growth with system size.
- Absence of characteristic time scales in the thermodynamic limit.
Conclusions:
- The information exchange process in the XY model demonstrates emergent criticality.
- Dynamic exponents characterize the information exchange mechanism, comparable to the Ising model.
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