Nematic liquid crystals: A monte carlo simulation study in higher dimensions

The Lebwohl-Lasher model of the isotropic-nematic phase transition in liquid crystals is studied in higher dimensions, by Monte Carlo computer simulations on simple cubic lattices. The transition is found to become increasingly first-order, and rapidly approaches the mean-field results, which are exact in infinitely many dimensions. The discontinuities in internal energy and order parameter are measured by careful analysis of the computer simulation data, and the free energy of each system is calculated. An empirical scaling law is also found to describe the shift of the transition temperature from the mean-field theory result. To distinguish the effects of coordination number from those of dimension and connectivity, a simulation of an f.c.c. lattice in d = 3 dimensions is performed. In addition, a partial analysis is made of finite-size effects in the six-dimensional simulation.