  We study the superfluid properties of attractively interacting fermions
hopping in a family of 2D and 3D lattices in the presence of synthetic gauge
fields having \pi-flux per plaquette. The reason for such a choice is that the
\pi-flux cubic lattice displays Dirac points and that decreasing the hopping
coefficient in a spatial direction (say, t_z) these Dirac points are unaltered:
it is then possible to study the 3D-2D interpolation towards the \pi-flux
square lattice. We also consider the lattice configuration providing the
continuous interpolation between the 2D \pi-flux square lattice and the
honeycomb geometry. We investigate by a mean field analysis the effects of
interaction and dimensionality on the superfluid gap, chemical potential and
critical temperature, showing that these quantities continuously vary along the
patterns of interpolation. In the two-dimensional cases at zero temperature and
at half filling there is a quantum phase transition occurring at a critical
(negative) interaction U_c presenting a linear critical exponent for the gap as
a function of |U-U_c|. We show that in three dimensions this quantum phase
transition is again retrieved, pointing out that the critical exponent for the
gap changes from 1 to 1/2 for each finite value of t_z.
