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Coercivity Landscape Characterizes Dynamic Hysteresis
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 model driven periodically by an external field . For large systems with small noise strength , we find the coercivity sequentially exhibits distinct behaviors with increasing driving rate : -scaling increase, stable plateau (), -scaling increase, and abrupt decline to disappearance. The plateau reflects the competition between thermodynamic and quasistatic limits, namely, , and . Here, is exactly the field-driven first-order phase transition point. In the post-plateau regime, scales with with and being the reference points of the plateau. Moreover, we reveal a finite-size scaling for the coercivity plateau as and 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.