Emergent Potts Order in a Coupled Hexatic-Nematic XY model

TL;DR

This study uses large-scale Monte Carlo simulations to reveal a novel composite Potts order in a coupled hexatic-nematic XY model, explaining the smectic-A' phase in liquid crystal films through a multi-step melting process.

Contribution

It introduces the concept of composite Potts $ ext{Z}_3$ order in a coupled XY model, providing a new theoretical explanation for the smectic-A' phase in liquid crystals.

Findings

Identification of a small region with composite Potts order above vortex binding transition.

Observation of algebraic hexatic and nematic order at lower temperatures.

Correlation of the phase behavior with experimental specific heat anomalies.

Abstract

Addressing the nature of an unexpected smectic-A' phase in liquid crystal 54COOBC films, we perform large scale Monte Carlo simulations of a coupled hexatic-nematic XY model. The resulting finite-temperature phase diagram reveals a small region with composite Potts $\mathbb{Z}_3$ order above the vortex binding transition; this phase is characterized by relative hexatic-nematic ordering though both variables are disordered. The system develops algebraic hexatic and nematic order only at a lower temperature. This multi-step melting scenario agrees well with the experimental observations of a sharp specific heat anomaly that emerges above the onset of hexatic positional order. We therefore propose that the smectic-A' phase is characterized by composite Potts order and bound-states of fractional vortices.