We have simulated the properties of 256 cylindrically symmetric particles interacting via a simple anisotropic potential of the form u
2
(r
12
) P
2
(cos B
12
) and with a scalar Lennard-Jones 12:6 potential, using the Monte Carlo technique. The simulations were performed for two forms of u2(r12) in the isothermal-isobaric ensemble and yielded values for volume, enthalpy, second-rank orientational order parameter, radial distribution function and second-rank angular correlation function. The specific heat at constant pressure, isothermal compressibility and isobaric expansivity were also obtained but they are subject to considerable error because they were evaluated from fluctuations. The system is found to exhibit a weak, firstorder transition from a nematic to an isotropic phase on increasing the temperature. The isotropic phase possesses short-range spatial and orientational order; it differs from the nematic phase, which has longrange orientational order but only short-range spatial order. The results of these simulations are used to discuss the influence of the range of the anisotropic potential on the behaviour of the nematogen. Previous Monte Carlo simulations of nematic liquid crystals had employed a lattice model with the anisotropic interactions restricted to nearest neighbours. Our results are used to study the effect of these convenient but unrealistic restrictions on the properties of the nematic. The results of our simulations are in reasonable accord with the properties of the nematogen, 4,4'- dimethoxyazoxybenzene, although no attem pt was made to select a pair potential to mimic the behaviour of any substance. Finally, we use the results of our simulations to test the validity of the molecular field approximation, as applied to nematics. This approximation is one of the foundations of the Maier-Saupe theory and its predictions are compared with the behaviour of the simulated nematics. It would appear that this theory provides a better description of our system than the lattice model, with its enforced spatial order and truncated anisotropic pair potential.
Extracting free energy of clusters in concentrated binary alloys from atomistic Monte Carlo simulations
