A ferromagnet modeled as a collection of bistable units (hysterons), each with up/down switching fields (α, β). The macroscopic magnetization is M = ∫∫ μ(α,β)·m(α,β,H) dα dβ. Minor loops and return-point memory emerge naturally.
The Preisach model (1935) discretizes the material into N independent hysterons: each switches up at field α and down at field β < α. The weight function μ(α,β) (here Gaussian) encodes the distribution of switching fields. The return-point memory property means that after any cyclic field history, the magnetization returns exactly to the same state — a non-trivial topological property of the Preisach operator.