Nematic phase transitions in two-dimensional systems

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 $P\mathrm{\_}4$. The system is studied through standard Finite-Size Scaling and conformal rescaling of density profiles or correlation functions. The low temperature limit is discussed in the spin wave approximation and confirms the numerical results, while the value of the correlation function exponent at the deconfining transition seems controversial.