Hysteresis in Ferromagnetic Random Field Ising Model with an Arbitrary Initial State

TL;DR

This paper derives exact formulas for hysteresis loops in a ferromagnetic random field Ising model on a Bethe lattice, considering any initial spin configuration, thus generalizing previous results limited to uniform initial states.

Contribution

It provides the first exact expressions for hysteresis in the RFIM with arbitrary initial states on a Bethe lattice, extending prior work restricted to uniform initial conditions.

Findings

Exact hysteresis expressions for arbitrary initial states.

Generalization of previous models to non-uniform initial conditions.

Applicable at zero temperature and zero driving frequency.

Abstract

We present exact expressions for hysteresis loops in the ferromagnetic random field Ising model in the limit of zero temperature and zero driving frequency for an arbitrary initial state of the model on a Bethe lattice. This work extends earlier results that were restricted to an initial state with all spins pointing parallel to each other.