A MODEL FOR 2-DIMENSIONAL ORIENTATIONAL ORDER

We use a generalization of Kikuchi's cluster variational method (CVM), in the pair approximation, to study anisotropic plane rotors on a square lattice as a simple model for two dimensional nematics. The system was shown to exhibit nematic ordered states at low temperature, disordering, for all anisotropies, through a continuous transition. The orientational distribution functions, order parameter, internal energy and specific heat were calculated within the CVM and compared with the results of a recent computer simulation. Estimates for the non-classical exponents were obtained using a mean field renormalization group analysis. A spin wave argument was also used to investigate the role of long range fluctuations near the isotropic fixed point. The accuracy of these different techniques is discussed within the context of our model.