  We consider a non-local free energy functional, modelling a competition
between entropy and pairwise interactions reminiscent of the second order
virial expansion, with applications to nematic liquid crystals as a particular
case. We build on previous work on understanding the behaviour of such models
within the large-domain limit, where minimisers converge to minimisers of a
quadratic elastic energy with manifold-valued constraint, analogous to harmonic
maps. We extend this work to establish H\"older bounds for (almost-)minimisers
on bounded domains, and demonstrate stronger convergence of (almost)-minimisers
away from the singular set of the limit solution. The proof techniques bear
analogy with recent work of singularly perturbed energy functionals, in
particular in the context of the Ginzburg-Landau and Landau-de Gennes models.
