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This study explores hysteresis dynamics in the stochastic ϕ⁴ model. We reveal distinct scaling behaviors of coercivity across timescales, including a plateau phase, and uncover finite-time and finite-size effects in nonequilibrium systems.

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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.