Topology and nematic ordering

We consider the weakly first-order phase transition between the isotropic and ordered phases of nematics in terms of the behavior of topological line defects. Specifically, we present analytical and Monte Carlo results for a new coarse-grained theory of nematics which incorporates the inversion symmetry of nematics as a local gauge invariance. Increasing the disclination core energy makes the nematic-isotorpic transition more weakly first order, and eventually splits it into two continuous transitions which involve the unbinding and condensation of defects, respectively. We find a novel isotropic phase with toplogical order.