  Using systematic effective field theory, we explore the properties of
antiferromagnetic films subjected to magnetic and staggered fields that are
either mutually aligned or mutually orthogonal. We provide low-temperature
series for the entropy density in either case up to two-loop order. Invoking
staggered, uniform and sublattice magnetizations of the bipartite
antiferromagnet, we investigate the subtle order-disorder phenomena in the spin
arrangement, induced by temperature, magnetic and staggered fields -- some of
which are quite counterintuitive. In the figures we focus on the
spin-$\frac{1}{2}$ square-lattice antiferromagnet, but our results are valid
for any other bipartite two-dimensional lattice.
