Enhancement of nematic order and global phase diagram of a lattice model for coupled nematic systems

We use an infinite-range Maier-Saupe model, with two sets of local quadrupolar variables and restricted orientations, to investigate the global phase diagram of a coupled system of two nematic subsystems. The free energy and the equations of state are exactly calculated by standard techniques of statistical mechanics. The nematic-isotropic transition temperature of system A increases with both the interaction energy among mesogens of system B, and the two-subsystem coupling $J$. This enhancement of the nematic phase is manifested in a global phase diagram in terms of the interaction parameters and the temperature $T$. We make some comments on the connections of these results with experimental findings for a system of diluted ferroelectric nanoparticles embedded in a nematic liquid-crystalline environment.