Field-induced uniaxial and biaxial nematic phases in the Maier-Saupe-Zwanzig (MSZ) lattice model

We report detailed statistical mechanics calculations to analyse the field-temperature phase diagram of a fully connected Maier-Saupe-Zwanzig (MSZ) lattice model for the nematic transitions in liquid-crystalline systems. If the field is applied along the uniaxial direction, with positive anisotropy, there is a first-order boundary between distinct uniaxial paranematic phases, which ends at a simple critical point. For negative values of the anisotropy, the first-order boundary becomes continuous at a tricritical point, and the transition is between field-induced uniaxial and biaxial structures. This elementary MSZ lattice model provides a way to systematically regain all of the main features of earlier phenomenological and model calculations. Due to the simplicity of the calculations, critical and tricritical points, as well as critical lines, can be located analytically, which leads to a possibility of comparisons with values for real experimental systems. Also, we formulate a generalised six-state MSZ model, which takes into account intrinsic molecular biaxiality, and perform calculations to determine the location of the critical point in the field-temperature phase diagram.