A Finite Dimensional Model Problem in Ferromagnetism

In this article we calculate magnetic equilibria of a finite dimensional model of a polycrystalline ferromagnetic body. Our model incorporates recent advances on frustration and microstructure in ferromagnetism. In particular, we will use minimizing sequences or Young- measures to model equilibrium states, and we make use of nonlocal exchange energies. We show that our model problem has a rich class of relative equilibria. Furthermore, this set of solutions can be interpreted as representing a quasistatic hysteresis diagram that exhibits hysteresis subloops and the Barkhausen effect.