The magnetization-driven random field Ising model at T=0

TL;DR

This paper investigates the zero-temperature hysteretic behavior of the random field Ising model under magnetization control, comparing microscopic trajectories and energy properties across different lattice structures and protocols.

Contribution

It introduces a magnetization-driven protocol for the RFIM at T=0 and compares its microscopic and energetic properties with the traditional field-driven approach.

Findings

Energy inside macroscopic avalanches matches analytical predictions on the Bethe lattice.

Output field fluctuations are large and non-self-averaging.

Energy U(M) is consistent across protocols when no avalanches occur.

Abstract

We study the hysteretic evolution of the random field Ising model (RFIM) at T=0 when the magnetization M is controlled externally and the magnetic field H becomes the output variable. The dynamics is a simple modification of the single-spin-flip dynamics used in the H-driven situation and consists in flipping successively the spins with the largest local field. This allows to perform a detailed comparison between the microscopic trajectories followed by the system with the two protocols. Simulations are performed on random graphs with connectivity z=4 (Bethe lattice) and on the 3-D cubic lattice. The same internal energy U(M)is found with the two protocols when there is no macroscopic avalanche and it does not depend on whether the microscopic states are stable or not. On the Bethe lattice, the energy inside the macroscopic avalanche also coincides with the one that is computed analytically with the H-driven algorithm along the unstable branch of the hysteresis loop. The output field, defined here as dU/dM, exhibits very large fluctuations with the magnetization and is not self-averaging. Relation to the experimental situation is discussed.