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.

• Received 14 October 2004

DOI:https://doi.org/10.1103/PhysRevE.72.031711