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

TL;DR

This paper analyzes the scaling behavior of coercivity in dynamic hysteresis across different regimes and system sizes, providing analytical and numerical insights into the phenomenon.

Contribution

It offers detailed proofs and numerical evidence for the coercivity landscape in the stochastic $$ model and explores finite-size effects in magnetic hysteresis.

Findings

Plateau features in coercivity landscape at characteristic rate $v_P$.

Different scaling laws for coercivity below and above the plateau.

Finite-time coercivity scaling shows model-specific behavior in the fast-driving regime.

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 $\phi^4$ 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 ($v_H<v_P$), the $H_c\sim v_H$ scaling obtained in the near-equilibrium regime becomes inaccessible in the thermodynamic limit. Above the plateau ($v_H>v_P$), scaling in the fast-driving regime, $H_c\sim v_H^{1/2}$, is completely different from that, $H_c-H_P\sim (v_H-v_P)^{2/3}$, 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.