Influence of the driving mechanism on the response of systems with athermal dynamics: the example of the random-field Ising model

TL;DR

This study examines how different driving mechanisms affect the hysteretic response of athermal systems, specifically the random-field Ising model, revealing distinct behaviors depending on disorder strength and driving protocol.

Contribution

It compares the effects of controlling external magnetic field versus magnetization on hysteresis in the RFIM, highlighting differences at low and high disorder levels.

Findings

At high disorder, hysteresis loops are identical for both protocols.

At low disorder, M-driven loops are re-entrant with intermittent fluctuations.

Results relate to experimental behaviors in disordered magnetic and shape memory materials.

Abstract

We investigate the influence of the driving mechanism on the hysteretic response of systems with athermal dynamics. In the framework of local-mean field theory at finite temperature (but neglecting thermallly activated processes), we compare the rate-independent hysteresis loops obtained in the random field Ising model (RFIM) when controlling either the external magnetic field $H$ or the extensive magnetization $M$. Two distinct behaviors are observed, depending on disorder strength. At large disorder, the $H$-driven and $M$-driven protocols yield identical hysteresis loops in the thermodynamic limit. At low disorder, when the $H$-driven magnetization curve is discontinuous (due to the presence of a macroscopic avalanche), the $M$-driven loop is re-entrant while the induced field exhibits strong intermittent fluctuations and is only weakly self-averaging. The relevance of these results to the experimental observations in ferromagnetic materials, shape memory alloys, and other disordered systems is discussed.