Approximate dynamical eigenmodes of the Ising model with local spin-exchange moves

Area of Science:

• Statistical Mechanics
• Condensed Matter Physics

Background:

• The two-dimensional Ising model is a fundamental model in statistical mechanics.
• Understanding critical phenomena and dynamics is crucial for condensed matter physics.

Purpose of the Study:

• To identify the dynamical eigenmodes of the 2D Ising model at critical temperature.
• To investigate the dynamical scaling properties and anomalous diffusion of magnetization.
• To verify the fluctuation-dissipation theorem using a generalized Langevin equation.

Main Methods:

• Analyzing Fourier modes of magnetization as dynamical eigenmodes.
• Calculating dynamical scaling properties for these modes.
• Computing autocorrelation functions and mean-square deviation of line magnetizations.
• Applying the generalized Langevin equation with a memory kernel.

Main Results:

• Fourier modes of magnetization are confirmed as dynamical eigenmodes for Kawasaki dynamics.
• Anomalous diffusion of line magnetization is observed at intermediate times (1≲t≲L^{z_{c}}).
• The generalized Langevin equation accurately describes the anomalous diffusion.
• The fluctuation-dissipation theorem is verified through force autocorrelation function calculations.

Conclusions:

• The study establishes Fourier modes as key dynamical components in the 2D Ising model.
• Anomalous diffusion is a significant feature of magnetization dynamics near criticality.
• The generalized Langevin equation provides a consistent framework for understanding these dynamics and their relation to thermodynamics.