Coercivity Landscape Characterizes Dynamic Hysteresis

TL;DR

This paper investigates the dynamic behaviors of hysteresis in the stochastic $$ model under periodic driving, revealing distinct scaling regimes, phase transition points, and finite-size effects through theoretical and numerical analysis.

Contribution

It introduces a comprehensive characterization of coercivity and hysteresis scaling behaviors across different driving rates and system sizes, connecting them to phase transition phenomena.

Findings

Identifies multiple scaling regimes of coercivity with increasing driving rate.

Discovers a plateau in coercivity reflecting competition between thermodynamic and quasi-static limits.

Establishes finite-size scaling laws for the coercivity plateau using renormalization-group theory.

Abstract

Hysteresis, with rich dynamical behaviors-especially in interacting systems-has drawn broad research interest. Yet its dynamic scalings across time scales lack a unified description, and their transitions remain unclear. Here, we study the stochastic $\phi^4$ model driven periodically by an external field $H$. For large systems with small noise strength $\sigma$, we find the coercivity $H_c \equiv H(\langle\phi\rangle=0)$ sequentially exhibits distinct behaviors with increasing driving rate $v_H$: $v_H$-scaling increase, stable plateau ($v_H^0$), $v_H^{1/2}$-scaling increase, and abrupt decline to disappearance. The plateau reflects the competition between thermodynamic and quasi-static limits, namely, $\lim_{\sigma\to 0}\lim_{v_H\to 0}H_c = 0$, and $\lim_{v_H\to 0}\lim_{\sigma\to 0}H_c=H^*$. Here, $H^*$ is exactly the field-driven first-order phase transition point. In the post-plateau regime, $(H_{c} - H_{P})$ scales with $(v_{H} - v_{P})^{2/3}$ with $v_{P}$ and $H_{P}$ being the reference points of the plateau. Moreover, we reveal a finite-size scaling for the coercivity plateau as $v_{P}\sim\sigma^{2}$ and $(H^*-H_P)\sim\sigma^{4/3}$ by utilizing renormalization-group theory. Our work provides a panoramic view of finite-time scalings of the hysteresis and offers new insights into finite-time/finite-size effect interplay in non-equilibrium systems.