Liquid crystals in two dimensions: First-order phase transitions and nonuniversal critical behavior

TL;DR

This paper investigates phase transitions in two-dimensional liquid crystals, revealing a first-order transition with small line tension under certain conditions, and a continuous, non-universal critical transition resembling the 2D Potts model when interactions are broader.

Contribution

It demonstrates the conditions under which two-dimensional liquid crystals exhibit first-order versus continuous phase transitions and characterizes their critical behavior.

Findings

First-order transition with small line tension and strong interface fluctuations.

Transition becomes continuous with non-universal critical behavior.

Critical behavior approximately matches the two-dimensional Potts model.

Abstract

Liquid crystals in two dimensions undergo a first-order isotropic-to-quasi-nematic transition, provided the particle interactions are sufficiently ``sharp and narrow''. This implies phase coexistence between isotropic and quasi-nematic domains, separated by interfaces. The corresponding line tension is determined, and shown to be very small, giving rise to strong interface fluctuations. When the interactions are no longer ``sharp and narrow'', the transition becomes continuous, with non-universal critical behavior obeying hyperscaling, and approximately resembling the two-dimensional Potts model.