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Updated: Jul 15, 2026
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Age-dependent Dynamics of Locomotion in Caenorhabditis elegans: A Lyapunov Exponent Analysis
Published on: September 23, 2025
Short-time critical dynamics and aging phenomena in the two-dimensional XY model
1Zhejiang Institute of Modern Physics, Zhejiang University, Hangzhou 310027, People's Republic of China.
Summary
We simulated dynamic relaxation in the 2D XY model near its phase transition, revealing distinct aging behaviors and correlation length corrections based on initial states. These findings clarify complex system dynamics.
Area of Science:
- Statistical Mechanics
- Condensed Matter Physics
Background:
- The two-dimensional XY model is a fundamental system for studying phase transitions.
- Understanding dynamic relaxation processes is crucial for characterizing critical phenomena.
Purpose of the Study:
- To investigate dynamic relaxation processes in the 2D XY model at and below the Berezinskii-Kosterlitz-Thouless transition temperature.
- To analyze aging phenomena and their dependence on initial system states (ordered vs. disordered).
- To extract scaling functions of the two-time correlation function.
Main Methods:
- Monte Carlo simulations were employed to model the dynamic relaxation.
- Simulations were performed starting from both ordered and disordered initial configurations.
- The two-time correlation function A(t',t) was measured to probe system dynamics.
- Spatial correlation length xi(t) was analyzed for different initial states.
Main Results:
- Distinct aging phenomena were observed depending on the initial state.
- Power-law corrections in xi(t) were found for ordered initial states.
- Logarithmic corrections in xi(t) were identified for disordered initial states.
- Scaling functions for A(t',t) were successfully extracted.
Conclusions:
- The study highlights the significant impact of initial conditions on dynamic relaxation and aging in the 2D XY model.
- The observed corrections to correlation length provide insights into the critical dynamics near the BKT transition.
- Extracted scaling functions offer a universal description of the two-time correlation function during relaxation.
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