  Barkhausen noise as found in magnets is studied both with and without the
presence of long-range (LR) demagnetizing fields using the non-equilibrium,
zero-temperature random-field Ising model. Two distinct subloop behaviors arise
and are shown to be in qualitative agreement with experiments on thin film
magnets and soft ferromagnets. With LR fields present subloops resemble a
self-organized critical system, while their absence results in subloops that
reflect the critical point seen in the saturation loop as the system disorder
is changed. In the former case, power law distributions of noise are found in
subloops, while in the latter case history-induced critical scaling is studied
in avalanche size distributions, spin-flip correlation functions, and
finite-size scaling of the second moments of the size distributions. Results
are presented for simulations of over 10^8 spins.
