  We examine different models and methods for studying finite-temperature
magnetic hysteresis in nanoparticles and ultrathin films. This includes
micromagnetic results for the hysteresis of a single magnetic nanoparticle
which is misaligned with respect to the magnetic field. We present results from
both a representation of the particle as a one-dimensional array of magnetic
rotors, and from full micromagnetic simulations. The results are compared with
the Stoner-Wohlfarth model. Results of kinetic Monte Carlo simulations of
ultrathin films are also presented. In addition, we discuss other topics of
current interest in the modeling of magnetic hysteresis in nanostructures,
including kinetic Monte Carlo simulations of dynamic phase transitions and
First-Order Reversal Curves.
