A Monte Carlo investigation of the planar Lebwohl-Lasher lattice model

A Monte Carlo computer simulation of a planar version of the Lebwohl-Lasher model is presented. The model consists of a set of interaction centres forming a simple square lattice. The pair potential is nearest-neighbours, attractive, and varies as a second Legendre polynomial of the relative orientation between the two particles. Five lattice sizes, 5 × 5, 10 × 10, 20 × 20, 60 × 60 and 80 × 80, of this two-dimensional system have been simulated with Monte Carlo and periodic boundary conditions. A study of the orientational pair correlation function indicates a power law decay in the ordered phase and an exponential decay above the pseudo-transition temperature. Our results are consistent with the absence of a true phase transition but also indicate a low-temperature phase with long short-range order. Comparisons are made with one existing simulation and with the mean field theory results.