Maier-Saupe nematogenic fluid interacting with an isotropic and an anisotropic Yukawa potentials: field theory description

We adopt a field-theoretical approach to study equilibrium properties of a homogeneous Maier-Saupe nematogenic fluid interacting with an isotropic and an anisotropic Yukawa potentials. In the mean field approximation, we retrieve the standard Maier-Saupe theory for nematic liquid crystals. Beyond the mean field approximation, we show that the repulsive isotropic potential plays an important role in the description of the nematic phase. In the Gaussian approximation analytical expressions for the correlation functions, the free energy, the pressure, and the elasticity constant are derived. We establish a simple condition on the parameters of the isotropic potential for the correlation functions and thermodynamic properties to be defined in the nematic phase. Subsequently, we find corrections to the single-particle distribution function and the order parameter due to fluctuations.