Dynamical critical behavior of the two-dimensional three-state Potts model

Area of Science:

• Statistical Physics
• Complex Systems Dynamics
• Computational Physics

Background:

• Understanding critical phenomena in statistical models is crucial for diverse fields.
• Dynamical critical behavior, particularly in systems with distinct equilibrium universality classes, remains an active research area.
• Previous studies on the 2D Ising ferromagnet hinted at shared dynamical exponents.

Purpose of the Study:

• To investigate the dynamical critical behavior of the two-dimensional three-state Potts model using single spin-flip dynamics.
• To analyze the time evolution of mean-squared deviation of magnetization (MSD_{M}) and magnetization autocorrelation function.
• To compare the observed dynamical behavior with that of the two-dimensional Ising ferromagnet.

Main Methods:

• Numerical simulations of the two-dimensional three-state Potts model.
• Analysis of the mean-squared deviation of magnetization (MSD_{M}) over time.
• Calculation of the magnetization autocorrelation function and identification of crossover times and dynamical regimes.

Main Results:

• Identified two crossover behaviors at times τ_{1}∼L^{z_{1}} and τ_{2}∼L^{z_{2}}, defining three distinct dynamical regimes.
• Observed MSD_{M} transitioning from ordinary diffusion to anomalous diffusion, then to a constant value.
• Magnetization autocorrelation function showed transitions between exponential and stretched-exponential decay across regimes, with shared exponents z_{1} and z_{2} with the Ising model, despite different equilibrium universality classes.

Conclusions:

• The two-dimensional three-state Potts model exhibits dynamical critical behavior characterized by two dynamic critical exponents, similar to the Ising model.
• The observed shared exponents (z_{1}, z_{2}) suggest that dynamical properties may transcend distinct equilibrium universality classes.
• The anomalous exponent α is not shared between the models, consistent with theoretical requirements.