Hysteresis-Loop Criticality in Disordered Ferromagnets-A Comprehensive Review of Computational Techniques

Disordered ferromagnets with a domain structure that exhibit a hysteresis loop when driven by the external magnetic field are essential materials for modern technological applications. Therefore, the understanding and potential for controlling the hysteresis phenomenon in these materials, especially concerning the disorder-induced critical behavior on the hysteresis loop, have attracted significant experimental, theoretical, and numerical research efforts. We review the challenges of the numerical modeling of physical phenomena behind the hysteresis loop critical behavior in disordered ferromagnetic systems related to the non-equilibrium stochastic dynamics of domain walls driven by external fields. Specifically, using the extended Random Field Ising Model, we present different simulation approaches and advanced numerical techniques that adequately describe the hysteresis loop shapes and the collective nature of the magnetization fluctuations associated with the criticality of the hysteresis loop for different sample shapes and varied parameters of disorder and rate of change of the external field, as well as the influence of thermal fluctuations and demagnetizing fields. The studied examples demonstrate how these numerical approaches reveal new physical insights, providing quantitative measures of pertinent variables extracted from the systems' simulated or experimentally measured Barkhausen noise signals. The described computational techniques using inherent scale-invariance can be applied to the analysis of various complex systems, both quantum and classical, exhibiting non-equilibrium dynamical critical point or self-organized criticality.