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

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.

11 pages, 13 figures

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• Diversity-induced resonance in a model for opinion formation
• Influence of the driving mechanism on the response of systems with athermal dynamics: the example of the random-field Ising model
• Hysteresis and complexity in the zero-temperature mean-field RFIM: the soft-spin version
• Stable, metastable and unstable states in the mean-field RFIM at T=0
• Hysteresis in Anti-Ferromagnetic Random-Field Ising Model at Zero Temperature
• Modelling avalanches in martensites