  Local magnetic ordering in artificial spin ices is discussed from the point
of view of how geometrical frustration controls dynamics and the approach to
steady state. We discuss the possibility of using a particle picture based on
vertex configurations to interpret time evolution of magnetic configurations.
Analysis of possible vertex processes allows us to anticipate different
behaviors for open and closed edges and the existence of different field
regimes. Numerical simulations confirm these results and also demonstrate the
importance of correlations and long range interactions in understanding
particle population evolution. We also show that a mean field model of vertex
dynamics gives important insights into finite size effects.
