*C. Chiccoli, P. Pasini, C. Zannoni**, Phase diagram and orientational order of a system with
second and fourth rank interactions, Int. J. Mod. Phys. B, 11, 1937-1944 (1997) *

*A simple nearest neighbour generalized Lebwohl - Lasher model for liquid crystals, where a fourth rank interaction
is added to the usual second rank one, is investigated in detail.*

*U _{ij}= _{ij }[P_{2}(cos _{ij} ) + c_{4} P_{4}(cos _{ij} )]*

*We have obtained the phase diagram of the system performing extensive Monte Carlo computer simulations for
a range of the fourth to the second rank relative strengths and we compare it with the prediction of Mean Field
and Two Site Cluster theories. We show that the addition of a non-negligible fourth rank term significantly changes
the temperature dependence of the order parameter. Fourth rank contributions larger than 20 % worsen the agreement
of the model with the typical temperature behavior of the order in nematics.*

*Order parameter <P _{2}>versus reduced temperature T*=T/T_{NI }.The curves correspond
to Haller law : <P_{2}>= (1 - T*)
+ <P_{2}>_{iso }and the exponent is determined experimentally to be between 0.17 and 0.25 for many Schiff bases and
cyanobiphenyl nematics[a,b]*

*[(a)F. Leenhouts, W.H. de Jeu and A.J. Dekker, J. de Physique, 40, 989 (1979).*

*(b) S.T. Wu and R.J. Cox, J. Appl. Phys., 64, 821 (1988).]*