Topological transition in a two-dimensional model of liquid crystal

Simulations of nematic-isotropic transition of liquid crystals in two dimensions are performed using an O2 vector model characterized by nonlinear nearest neighbor spin interaction governed by the fourth Legendre polynomial P4. 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.