  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 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.
