Coercivity Landscape Characterizes Dynamic Hysteresis

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 $\ddot{I}{•}^4$ model driven periodically by an external field $H$. For large systems with small noise strength $\ddot{I}ƒ$, we find the coercivity $H_c\equiv H(⟨\ddot{I}•⟩=0)$ 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, ${\lim }_{\ddot{I}ƒ\to 0}{\lim }_{v_H\to 0}{H}_c=0$, and ${\lim }_{v_H\to 0}{\lim }_{\ddot{I}ƒ\to 0}{H}_c=H^{\ast }$. Here, $H^{\ast }$ 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 $v_P\sim \ddot{I}{ƒ}^2$ and $(H^{\ast }-H_P)\sim \ddot{I}{ƒ}^{4/3}$ 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.

Accepted version. To be published in Phys. Rev. Lett