  Numerical solutions of the Landau-Lifshitz-Gilbert micromagnetic model
incorporating thermal fluctuations and dipole-dipole interactions (calculated
by the Fast Multipole Method) are presented for systems composed of nanoscale
iron pillars of dimension 9 nm x 9 nm x 150 nm. Hysteresis loops generated
under sinusoidally varying fields are obtained, while the coercive field is
estimated to be 1979 $\pm$ 14 Oe using linear field sweeps at T=0 K. Thermal
effects are essential to the relaxation of magnetization trapped in a
metastable orientation, such as happens after a rapid reversal of an external
magnetic field less than the coercive value. The distribution of switching
times is compared to a simple analytic theory that describes reversal with
nucleation at the ends of the nanomagnets. Results are also presented for
arrays of nanomagnets oriented perpendicular to a flat substrate. Even at a
separation of 300 nm, where the field from neighboring pillars is only $\sim$ 1
Oe, the interactions have a significant effect on the switching of the magnets.
