Topology and Nematic Ordering I: A Gauge Theory

TL;DR

This paper introduces a gauge theory approach to nematic phase transitions, revealing how topological defects influence the transition's nature and uncovering a novel isotropic phase with topological order.

Contribution

It develops a new lattice gauge theory for nematics, linking defect behavior to phase transition types and identifying a topologically ordered isotropic phase.

Findings

Transition becomes more weakly first order with higher disclination core energy.

Transitions split into two continuous phases in Ising and Heisenberg universality classes.

Discovery of a topologically ordered isotropic phase between the transitions.

Abstract

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. Analytical and Monte Carlo results are presented for a new coarse-grained lattice theory of nematics which 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.