Topological transition in a two-dimensional model of liquid crystal

TL;DR

This paper investigates a topological transition in a 2D liquid crystal model using simulations, revealing a phase change from paramagnetic to critical phase, supported by finite-size scaling and conformal rescaling analyses.

Contribution

It introduces a 2D O(2) vector model with P4 interaction to study liquid crystal phase transitions, highlighting a topological transition not previously characterized.

Findings

Identifies a topological transition between paramagnetic and critical phases.

Confirms numerical results with spin wave approximation.

Uses finite-size scaling and conformal rescaling techniques.

Abstract

Simulations of nematic-isotropic transition of liquid crystals in two dimensions are performed using an O(2) vector model characterised by non linear nearest neighbour spin interaction governed by the fourth Legendre polynomial $P\_4$. The system is studied through standard Finite-Size Scaling and conformal rescaling of density profiles of correlation functions. A topological transition between a paramagnetic phase at high temperature and a critical phase at low temperature is observed. The low temperature limit is discussed in the spin wave approximation and confirms the numerical results.