Corrections to scaling for the two-dimensional dynamic XY model.

Area of Science:

• Statistical physics
• Condensed matter physics
• Computational physics

Background:

• The two-dimensional XY model is a fundamental model in statistical mechanics.
• Understanding its dynamic relaxation properties is crucial for various physical phenomena.
• Scaling corrections influence the behavior of physical systems near critical points.

Purpose of the Study:

• To investigate the dynamic relaxation of the two-dimensional XY model.
• To identify and characterize scaling corrections in different initial states.
• To determine the dynamic exponent z.

Main Methods:

• Large-scale Monte Carlo simulations were employed.
• The simulations focused on the dynamic relaxation process.
• Analysis involved examining corrections to scaling from ordered and disordered initial states.

Main Results:

• A logarithmic correction to scaling was confirmed for relaxation from a disordered state.
• An inverse power law correction was observed for relaxation from an ordered state.
• The dynamic exponent z was determined to be 2.04(1).

Conclusions:

• The initial state significantly impacts the dynamic relaxation scaling in the 2D XY model.
• Logarithmic corrections are a key feature of relaxation from disordered states.
• The findings provide precise values for critical exponents in this model.