this paper we set out to consider the anisotropic pair potential U, = -,,,[ P2 (cos fio) + XPn(cos ,8o) ] , (2) where the parameter X gives the strength of the fourth-rank interaction relative to the second. As for the potential in eq. (1), the interaction constant is positive and equal to if particles i and j are first neighbours and is zero otherwise. The be- haviour of a system interacting through such a pair potential has been predicted using the molecular field approximation  and two site cluster methods [20,21]. The influence of the fourth-rank term on the transition temperature can be investigated using thermodynamic perturbation theory and we give such an analysis in the following section. The Monte Carlo simulations are described briefly in section 3 and the results of these simulations are G.J. Fuller et al. / Computer simulation studies of anisotroptt .ystemv presented in section 4. The' transitional properties and the temperature dependence of the internal energy. heat capacity at constant volume and the second-rank order parameter are compared with the predictions of the molecular field theory in section 5. Our conclusions are in section
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