  At low temperatures, some lattice spin models with simple ferromagnetic or
antiferromagnetic interactions (for example nearest-neighbour interaction being
isotropic in spin space on a bipartite three-dimensional lattice) produce
orientationally ordered phases exhibiting nematic (second--rank) order, in
addition to the primary first-rank one; on the other hand, in the Literature,
they have been rather seldom investigated in this respect. Here we study the
thermodynamic properties of a three-dimensional model with dipolar-like
interaction. Its ground state is found to exhibit full orientational order with
respect to a suitably defined staggered magnetization (polarization), but no
nematic second-rank order. Extensive Monte Carlo simulations, in conjunction
with Finite-Size Scaling analysis have been used for characterizing its
critical behaviour; on the other hand, it has been found that nematic order
does indeed set in at low temperatures, via a mechanism of order by disorder.
