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Coercivity Landscape Characterizes Dynamic Hysteresis

Miao Chen1,2,*, Xiu-Hua Zhao1,2,*, and Yu-Han Ma1,2,3,†

  • *These authors contributed equally to this work.
  • †Contact author: yhma@bnu.edu.cn

Phys. Rev. Lett. 136, 117102 – Published 19 March, 2026

DOI: https://doi.org/10.1103/5rg8-52gl

Abstract

Hysteresis, with rich dynamical behaviors—especially in interacting systems—has drawn broad research interest. Yet its dynamic scalings across timescales lack a unified description, and their transitions remain unclear. Here, we study the stochastic ϕ4 model driven periodically by an external field H. For large systems with small noise strength σ, we find the coercivity Hc≡H(⟨ϕ⟩=0) sequentially exhibits distinct behaviors with increasing driving rate vH: vH-scaling increase, stable plateau (vH0), vH1/2-scaling increase, and abrupt decline to disappearance. The plateau reflects the competition between thermodynamic and quasistatic limits, namely, limσ→0limvH→0Hc=0, and limvH→0limσ→0Hc=H*. Here, H* is exactly the field-driven first-order phase transition point. In the post-plateau regime, (Hc−HP) scales with (vH−vP)2/3 with vP and HP being the reference points of the plateau. Moreover, we reveal a finite-size scaling for the coercivity plateau as vP∼σ2 and (H*−HP)∼σ4/3 by utilizing renormalization-group theory. Our Letter provides a panoramic view of finite-time scalings of the hysteresis and offers new insights into the interplay between finite-time and finite-size effects in nonequilibrium systems.

Physics Subject Headings (PhySH)

See Also

Finite-time and finite-size scalings of coercivity in dynamic hysteresis

Miao Chen, Xiu-Hua Zhao, and Yu-Han Ma
Phys. Rev. E 113, 034124 (2026)

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