Zero-temperature ordering dynamics in a two-dimensional biaxial next-nearest-neighbor Ising model

Area of Science:

• Statistical Mechanics
• Condensed Matter Physics
• Computational Physics

Background:

• The behavior of magnetic systems after rapid temperature changes (quenches) is crucial for understanding non-equilibrium dynamics.
• Ising models are fundamental for studying phase transitions and critical phenomena.
• Next-nearest-neighbor interactions introduce complexities beyond standard Ising models.

Purpose of the Study:

• To investigate the zero-temperature dynamics of a 2D biaxial next-nearest-neighbor Ising model.
• To analyze the system's evolution, freezing behavior, and critical exponents for different interaction strengths (κ).
• To compare the observed dynamics with related models like the 2D ANNNI model.

Main Methods:

• Numerical simulations of the 2D biaxial next-nearest-neighbor Ising model.
• Quenching the system to zero temperature and observing its time evolution.
• Analysis of residual energy decay, persistence probability, autocorrelation functions, and freezing probability.
• Estimation of dynamical exponents (z) and persistence exponents (θ).

Main Results:

• For κ<1, the system remains in active, non-equilibrium states indefinitely.
• For κ≥1, the system can freeze into striped states, not always reaching the ground state.
• Distinct dynamical behaviors and critical exponents (z and θ) were identified for κ>1 and κ=1.
• Power-law decay of residual energy was observed for both κ>1 and κ=1.

Conclusions:

• The 2D biaxial next-nearest-neighbor Ising model exhibits rich non-equilibrium dynamics dependent on the interaction parameter κ.
• The system can get trapped in non-equilibrium states or freeze into specific configurations.
• The identified dynamical classes and exponents provide insights into the universality of phase transitions in complex magnetic systems.