Topology and nematic ordering. I. A gauge theory

Abstract

We consider the weakly first order phase transition between the isotropic and ordered phases of nematic liquid crystals in terms of the behavior of topological line defects. Analytical and Monte Carlo results are presented for a recently introduced coarse-grained lattice theory of nematics that incorporates nematic inversion symmetry as a local gauge invariance. The nematic-isotropic transition becomes more weakly first order as disclination core energy is increased, eventually splitting into two continuous transitions involving the unbinding and condensation of defects, respectively. These transitions are shown to be in the Ising and Heisenberg universality classes. A novel isotropic phase with topological order occurs between them. © 1995 The American Physical Society.