Coercivity Landscape Characterizes Dynamic Hysteresis

Area of Science:

• Statistical mechanics
• Condensed matter physics
• Non-equilibrium systems

Background:

• Hysteresis exhibits complex dynamics, particularly in interacting systems, but lacks unified descriptions of dynamic scaling across timescales.
• Understanding transitions in hysteresis dynamics is crucial for characterizing non-equilibrium phenomena.

Purpose of the Study:

• To investigate the dynamic scaling behaviors of coercivity in the stochastic ϕ⁴ model under periodic external field driving.
• To elucidate the transitions and underlying mechanisms of hysteresis dynamics across different timescales and system sizes.

Main Methods:

• Stochastic ϕ⁴ model simulation with periodic external field driving.
• Analysis of coercivity (H_c) as a function of driving rate (v_H) and noise strength (σ).
• Application of renormalization-group theory to reveal finite-size scaling relations.

Main Results:

• Coercivity (H_c) shows distinct scaling behaviors with driving rate (v_H): v_H-scaling, a stable plateau (v_H^0), v_H^{1/2}-scaling, and disappearance.
• The plateau regime arises from the interplay between thermodynamic and quasistatic limits, with H* representing the first-order phase transition point.
• Post-plateau coercivity follows (H_c - H_P) ~ (v_H - v_P)^{2/3}.
• Finite-size scaling reveals v_P ~ σ² and (H* - H_P) ~ σ^{4/3} for the coercivity plateau.

Conclusions:

• This work provides a comprehensive view of finite-time scaling in hysteresis dynamics.
• New insights into the interplay between finite-time and finite-size effects in non-equilibrium systems are offered.
• The findings contribute to a unified description of hysteresis dynamics and phase transitions in driven systems.