  Synthetic antiferromagnets with strong perpendicular anisotropy can be
modeled by layered Ising antiferromagnets. Accounting for the fact that in the
experimental systems the ferromagnetic layers, coupled antiferromagnetically
via spacers, are multilayers, we propose a description through Ising films
where ferromagnetic stacks composed of multiple layers are coupled
antiferromagnetically. We study the equilibrium and non-equilibrium properties
of these systems where we vary the number of layers in each stack. Using
numerical simulations, we construct equilibrium temperature$-$magnetic field
phase diagrams for a variety of cases. We find the same dominant features
(three stable phases, where one phase boundary ends in a critical end point,
whereas the other phase boundary shows a tricritical point at which the
transition changes from first to second order) for all studied cases. Using
time-dependent quantities, we also study the ordering processes that take place
after a temperature quench. The nature of long-lived metastable states are
discussed for thin films, whereas for thick films we compute the surface
autocorrelation exponent.
