The rigorous formula of Suzuki for correlation function of classical systems and Ising model is generalized and applied to the rotationally invariant Maier-Saupe Hamil-tonian of liquid crystals.The results show that the microscopic treatment of the correlation function and magnetic Cotton-Mouton coefficient by one of the authors is indeed correct within the approximation stated. The random phase approximation results of Vertogen and van der Meer is improved. A scheme to describe the thermodynamics of liquid crystals beyond the mean field approximation is proposed.