  We predict two new physical effects in arrays of single-domain nanomagnets by
performing simulations using a realistic model Hamiltonian and physical
parameters. First, we find hysteretic multicycles for such nanomagnets. The
simulation uses continuous spin dynamics through the Landau-Lifshitz-Gilbert
(LLG) equation. In some regions of parameter space, the probability of finding
a multicycle is as high as ~0.6. We find that systems with larger and more
anisotropic nanomagnets tend to display more multicycles. This result
demonstrates the importance of disorder and frustration for multicycle
behavior. We also show that there is a fundamental difference between the more
realistic vector LLG equation and scalar models of hysteresis, such as Ising
models. In the latter case, spin and external field inversion symmetry is
obeyed but in the former it is destroyed by the dynamics, with important
experimental implications.
