  Due to remarkable advances in colloid synthesis techniques, systems of
squares and cubes, once an academic abstraction for theorists and simulators,
are nowadays an experimental reality. By means of a free minimization of the
free-energy functional, we apply Fundamental Measure Theory to analyze the
phase behavior of parallel hard squares and hard cubes. We compare our results
with those obtained by the traditional approach based on the Gaussian
parameterization, finding small deviations and good overall agreement between
the two methods. For hard squares our predictions feature at intermediate
packing fraction a smectic phase, which is however expected to be unstable due
to thermal fluctuations. This implies that for hard squares the theory predicts
either a vacancy-rich second-order transition or a vacancy-poor weakly
first-order phase transition at higher density. In accordance with previous
studies, a second-order transition with a high vacancy concentration is
predicted for hard cubes.
