Slow quench dynamics of the Baxter-Wu model

Area of Science:

• Statistical Mechanics
• Condensed Matter Physics
• Dynamical Systems

Background:

• The Baxter-Wu model is a significant model in statistical mechanics.
• Understanding defect formation during phase transitions is crucial.
• The Kibble-Zurek (KZ) mechanism describes defect generation in systems quenched across critical points.

Purpose of the Study:

• To investigate the dynamical properties of the Baxter-Wu model under slow temperature quenches.
• To analyze the scaling behavior of excess defect density during cooling and heating processes.
• To compare observed dynamics with predictions from the Kibble-Zurek mechanism and coarsening dynamics.

Main Methods:

• Monte Carlo simulations were employed to model the Baxter-Wu system.
• Slow quenches (both cooling and heating) were simulated by gradually tuning temperature.
• Excess defect density was tracked to analyze scaling behaviors and compare with theoretical predictions.

Main Results:

• During cooling, excess defect density scaling in the critical region aligns with the Kibble-Zurek (KZ) mechanism.
• Post-impulse regime, defect density decay deviates from simple KZ and coarsening dynamics, showing power-law behavior.
• During heating from the ground state, KZ exponents match cooling scenarios, but a crossover regime with exponential decay precedes the adiabatic regime.
• Heating from non-ground ordered states shows scaling but exponents deviate from KZ predictions.

Conclusions:

• The Kibble-Zurek mechanism accurately describes initial defect formation in the Baxter-Wu model under slow quenches.
• System dynamics after the impulse regime, particularly during cooling and heating from non-ground states, exhibit complex behaviors not fully explained by existing theories.
• A distinct crossover regime with exponential decay is identified during heating, highlighting non-trivial post-impulse dynamics.