Liquid Crystals in Two Dimensions

The existence of liquid crystalline order in two dimensions is discussed. It is shown that, contrary to a previous contention, a theory based on the lowest-order approximation to the virial expansion of the free energy (the Onsager limit) indicates that a nematic ordering transition does occur. The effects of the fluctuations in order are considered, and it is shown that the usual elastic theories cannot hold in two dimensions. I attempt to construct a microscopic discussion based on the Bogoliubov inequality, but find that it cannot be applied straightforwardly to this case.