Concurrent Modeling of Magnetic Field Parameters, Crystalline Structures, and Ferromagnetic Dynamic Critical Behavior Relationships: Mean-Field and Artificial Neural Network Projections

Abstract

In this work, Artificial Neural Network (ANN) was used to model the dynamic behavior of ferromagnetic hysteresis derived from performing the mean-field analysis on the Ising model. The effect of field parameters and system structure (via coordination number) on dynamic critical points was elucidated. The Ising magnetization equation was drawn from mean-field picture where the steady hysteresis loops were extracted, and series of the dynamic critical points for constructing dynamic phase-diagram were depicted. From the dynamic critical points, the field parameters and the coordination number were treated as inputs whereas the dynamic critical temperature was considered as the output of the ANN. The input-output datasets were divided into training, validating and testing datasets. The number of neurons in hidden layer was varied in structuring ANN network with highest accuracy. The network was then used to predict dynamic critical points of the untrained input. The predicted and the targeted outputs were found to match well over an extensive range even for systems with different structures and field parameters. This therefore confirms the ANN capabilities and indicates the ANN ability in modeling the ferromagnetic dynamic hysteresis behavior for establishing the dynamic-phase-diagram.