  We consider a class of spin-type discrete systems and analyze their continuum
limit as the lattice spacing goes to zero. Under standard coerciveness and
growth assumptions together with an additional head-to-tail symmetry condition,
we observe that this limit can be conveniently written as a functional in the
space of $Q$-tensors. We further characterize the limit energy density in
several cases (both in 2 and 3 dimensions). In the planar case we also develop
a second-order theory and we derive gradient or concentration-type models
according to the chosen scaling.
