Quadrupolar analogue of the Ising model in the reaction field aproximation

We describe the nematic phase of liquid crystals by a model analogo to the Ising model which in the continuum limit describe the quadrupolar interaction between molecules, whose dipoles are supposed to ocupy fixed positions in space. Their orientation are described by the discrete spin variable through their projections on the orientation direction caractherized in the nematic phase by the director vector. We consider a magnetic field applied in the same direction. We apply to this system the random phase approximation (RPA) whose results are better than those obtained by the Meier-Saupe mean field theory. We treat the model within the reaction field approximation (RFA) introduct the short range correlations and obtain better results than those obtained by RPA, with a lower critic temperature. Finally, we compare our results with other ones presented in the literarure envolving other and approximations. (author)