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 O(2) vector model characterized by nonlinear nearest neighbor 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.