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Magnetization-driven random-field Ising model at T=0
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We study the hysteretic evolution of the random field Ising model 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 one 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 three-dimensional 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 U/ M, exhibits very large fluctuations with the magnetization
and is not self-averaging. The relation to the experimental situation is discussed.
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ILLA I TORTÓS, Xavier, et al. Magnetization-driven random-field Ising model at T=0. Physical Review B. 2006. Vol. 74, num. 22, pags. 224404-1-224404-10. ISSN 0163-1829. [consulted: 20 of August of 2026]. Available at: https://hdl.handle.net/2445/10564