  An important aspect of real ferromagnetic particles is the demagnetizing
field resulting from magnetostatic dipole-dipole interaction, which causes
large particles to break up into domains. Sufficiently small particles,
however, remain single-domain in equilibrium. This makes such small particles
of particular interest as materials for high-density magnetic recording media.
In this paper we use analytic arguments and Monte Carlo simulations to study
the effect of the demagnetizing field on the dynamics of magnetization
switching in two-dimensional, single-domain, kinetic Ising systems. For systems
in the ``Stochastic Region,'' where magnetization switching is on average
effected by the nucleation and growth of fewer than two well-defined critical
droplets, the simulation results can be explained by the dynamics of a simple
model in which the free energy is a function only of magnetization. In the
``Multi-Droplet Region,'' a generalization of Avrami's Law involving a
magnetization-dependent effective magnetic field gives good agreement with our
simulations.
