PHASE-DIAGRAM AND ORIENTATIONAL ORDER OF A SYSTEM WITH 2ND AND 4TH RANK INTERACTIONS

A simple generalized Lebwohl-Lasher model for liquid crystals, where a fourth rank interaction is added to the usual second rank one, is inv estigated in detail. We have obtained the phase diagram of the system performing extensive Monte Carlo computer simulations for a range of t he fourth to the second rank relative strengths and we compare it with the prediction of Mean Field and Two Site Cluster theories. We show t hat the addition of a non-negligible fourth rank term significantly ch anges the temperature dependence of the order parameter. Fourth rank c ontributions larger than 20% worsen the agreement of the model with th e typical temperature behavior of the order in nematics.