Lattice model for ordering in two-dimensional plastic crystals

We study the properties of a two-dimensional square lattice model in which each lattice site is occupied by an elliptical molecule which may point either horizontally or vertically. Molecules on neighbouring lattice sites interact via a potential function based on the ellipsoid contact function introduced by Perram and Wertheim. We show that this model has a set of second-order phase transitions as the lattice constant is varied. These transitions separate phases exhibiting both nematic and staggered ordering from orientationally disordered phases. We present the phase diagram for the model and discuss how it changes as the eccentricity of the ellipses is varied.