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

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

References in corpus (29)

• Brownian Carnot engine
• Stochastic thermodynamics under coarse-graining
• Thermodynamic metrics and optimal paths
• The power of a critical heat engine
• Probing a dissipative phase transition via dynamical optical hysteresis
• Non-Majorana Origin of the Half-Quantized Conductance Plateau in Quantum Anomalous Hall Insulator and Superconductor Hybrid Structures
• Anomalous Hall hysteresis in Tm3Fe5O12/Pt with strain-induced perpendicular magnetic anisotropy
• Quantum thermodynamic cycle with quantum phase transition
• Hysteresis and the dynamic phase transition in thin ferromagnetic films
• Experimental validation of the $1/\tau$ -scaling entropy generation in finite-time thermodynamics with dry air
• Analytical model for the approximation of hysteresis loop and its application to the scanning tunneling microscope
• Optimal operating protocol to achieve efficiency at maximum power of heat engines
• Collective advantages in finite-time thermodynamics
• Geodesic path for the minimal energy cost in shortcuts to isothermality
• Scaling properties of the relaxation time near the mean-field spinodal
• Asymptotic forms and scaling properties of the relaxation time near threshold points in spinodal-type dynamical phase transitions
• Finite-time dynamical phase transition in non-equilibrium relaxation
• Kinetic Spinodal Instabilities in the Mott Transition in V2O3: Evidence from Hysteresis Scaling and Dissipative Phase Ordering
• Loss separation for dynamic hysteresis in magnetic thin films
• Dynamic hysteresis at a noisy saddle-node shows power-law scaling but nonuniversal exponent
• A Minimal Model for Carnot Efficiency at Maximum Power
• Complete universal scaling in first-order phase transitions
• Temperature fluctuations in mesoscopic systems
• Finite-dimensional signature of spinodal instability in an athermal hysteretic transition
• Hysteresis in the Ising model with Glauber dynamics
• Ergodicity Breaking and Scaling Relations for Finite-Time First-Order Phase Transition
• Engineering Ratchet-Based Particle Separation via Shortcuts to Isothermality
• Dynamic Hysteresis Across a Dissipative Multi-Mode Phase Transition
• Minimizing Dissipation via Interacting Environments: Quadratic Convergence to Landauer Bound