Mean field and computer simulation study of a nematogenic lattice model including three-body interactions

By now, nematogenic lattice models have been extensively studied in the literature dealing with liquid crystals; they usually involve cylindrically symmetric (uniaxial) particles and pairwise additive interaction potentials. On the other hand, quantum mechanical perturbation theory shows that interatomic or intermolecular potentials are only approximately pairwise additive; the pairwise additivity approximation (PAA) of molecular interactions has been extensively and systematically used in the statistical mechanics of condensed matter, and has proven rather successful. As an attempt to move beyond the PAA in the simulation of mesogenic systems, we have considered here a nematogenic lattice model consisting of uniaxial particles, whose centres of mass are associated with a simple-cubic lattice, and whose interaction potentials consist of a pairwise additive dispersion (Nehring–Saupe) term, restricted to nearest neighbours (and already studied in the literature), plus a short-range triplet-additive one, i.e., the Kielich–Stogryn generalization of the Axilrod–Teller–Muto formula for three atoms. The model has been studied by Mean Field theory and Monte Carlo simulation; the three-body term was found to produce a recognizable quantitative effect on the nematic ordering transition.