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Abstract
We have considered a classical system, consisting of two component unit vectors (plane rotators) associated with a three dimensional, simple cubic lattice, and interacting via the nearest neighbour pair potential
where m is a positive integer, ε is a positive constant setting the temperature and energy scales, and {φ k } are the angles defining the orientation of the plane rotators in an arbitrary reference frame (which can be identified with the lattice frame). The two potential models Wm and - Wm possess essentially the same properties in the absence of an external field (spin-flip symmetry); moreover, all of the potential models Wm have the same partition function, and several mean values can be defined in a way which is independent of m. This model is known rigorously to possess a low temperature ordering transition, extensively simulated in the magnetic language (m = 1); we examined here the nematic interpretation (c = −1, m = 2), and compare with molecular field and two site cluster predictions; we have also investigated director fluctuations.