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We consider a non-local free energy functional, modelling a competitionbetween entropy and pairwise interactions reminiscent of the second ordervirial expansion, with applications to nematic liquid crystals as a particularcase. We build on previous work on understanding the behaviour of such modelswithin the large-domain limit, where minimisers converge to minimisers of aquadratic elastic energy with manifold-valued constraint, analogous to harmonicmaps. We extend this work to establish H\"older bounds for (almost-)minimiserson bounded domains, and demonstrate stronger convergence of (almost)-minimisersaway from the singular set of the limit solution. The proof techniques bearanalogy with recent work of singularly perturbed energy functionals, inparticular in the context of the Ginzburg-Landau and Landau-de Gennes models.

H\"older regularity and convergence for a non-local model of nematic liquid crystals in the large-domain limit