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| Format: | Preprint |
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2025
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| Accès en ligne: | https://arxiv.org/abs/2506.24035 |
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| _version_ | 1866910230415147008 |
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| author | Chen, Miao Zhao, Xiu-Hua Ma, Yu-Han |
| author_facet | Chen, Miao Zhao, Xiu-Hua Ma, Yu-Han |
| contents | 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 $ϕ^4$ model driven periodically by an external field $H$. For large systems with small noise strength $σ$, we find the coercivity $H_c \equiv H(\langleϕ\rangle=0)$ 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, $\lim_{σ\to 0}\lim_{v_H\to 0}H_c = 0$, and $\lim_{v_H\to 0}\lim_{σ\to 0}H_c=H^*$. 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 $v_{P}\simσ^{2}$ and $(H^*-H_P)\simσ^{4/3}$ 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_24035 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Coercivity Landscape Characterizes Dynamic Hysteresis Chen, Miao Zhao, Xiu-Hua Ma, Yu-Han Statistical Mechanics 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 $ϕ^4$ model driven periodically by an external field $H$. For large systems with small noise strength $σ$, we find the coercivity $H_c \equiv H(\langleϕ\rangle=0)$ 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, $\lim_{σ\to 0}\lim_{v_H\to 0}H_c = 0$, and $\lim_{v_H\to 0}\lim_{σ\to 0}H_c=H^*$. 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 $v_{P}\simσ^{2}$ and $(H^*-H_P)\simσ^{4/3}$ 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. |
| title | Coercivity Landscape Characterizes Dynamic Hysteresis |
| topic | Statistical Mechanics |
| url | https://arxiv.org/abs/2506.24035 |