On the critical behavior of two-dimensional liquid crystals

TL;DR

This study investigates the critical behavior of the 2D Lebwohl-Lasher model for liquid crystals, using numerical methods to analyze phase transition scenarios and finite-size scaling, concluding that no critical transition occurs.

Contribution

The paper provides a comprehensive numerical analysis of the 2D LL-model's phase behavior, favoring a crossover scenario over a phase transition, and compares it with XY and Heisenberg models.

Findings

No critical transition in the 2D LL-model.

Finite-size scaling supports crossover behavior.

Comparison with XY and Heisenberg models clarifies phase behavior.

Abstract

The Lebwohl-Lasher (LL) model is the traditional model used to describe the nematic-isotropic transition of real liquid crystals. In this paper, we develop a numerical study of the temperature behaviour and of finite-size scaling of the two-dimensional (2D) LL-model. We discuss two possible scenarios. In the first one, the 2D LL-model presents a phase transition similar to the topological transition appearing in the 2D XY-model. In the second one, the 2D LL-model does not exhibit any critical transition, but its low temperature behaviour is rather characterized by a crossover from a disordered phase to an ordered phase at zero temperature. We realize and discuss various comparisons with the 2D XY-model and the 2D Heisenberg model. Adding to previous studies of finite-size scaling behaviour of the order parameter and conformal mapping of order parameter profile, we analyze the critical scaling of the probability distribution function, hyperscaling relations and stiffness order parameter and conclude that the second scenario (no critical transition) is the most plausible.