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

2025/07/10 by Chen, Miao, Zhao, Xiu-Hua, Ma, Yu-Han
#FOS: Physical sciences #Statistical Mechanics (cond-mat.stat-mech)

paper · doi:10.48550/arxiv.2507.07933

Abstract

The coercivity panorama for characterizing the dynamic hysteresis in interacting systems across multiple timescales is proposed by Chen et al. in a companion paper. For the stochastic ϕ⁴ model under periodic driving of rate v_H, the coercivity landscape H_c(v_H) exhibits plateau features at a characteristic rate v_P with the corresponding coercivity H_P. Below this plateau (v_Hv_P), scaling in the fast-driving regime, H_c∼ v_H^1/2, is completely different from that, H_c-H_P∼ (v_H-v_P)^2/3, in the post-plateau slow-driving regime. The emergence of the plateau with a finite-size scaling reflects the competition between the thermodynamic limit and the quasi-static limit. In this paper, we provide detailed analytical proofs and numerical evidence supporting these results. Moreover, to demonstrate the coercivity panorama in concrete physical systems, we study the magnetic hysteresis in the Curie-Weiss model and analyze its finite-size effects. We reveal that finite-time coercivity scaling shows model-specific behavior only in the fast-driving regime, while exhibiting universal characteristics elsewhere.

Citations

• Complete Universal Scaling in First-Order Phase Transitions
• Ergodicity Breaking and Scaling Relations for Finite-Time First-Order Phase Transition

Related

• Coercivity Panorama of Dynamic Hysteresis
• Ergodicity Breaking and Scaling Relations for Finite-Time First-Order Phase Transition
• Memory effects and scaling laws in slowly driven systems
• Onset of reptations and critical hysteretic behavior in disordered systems
• Critical Hysteresis