A Monte Carlo simulation of the inhomogeneous Lebwohl-Lasher lattice model

Abstract

A Monte Carlo computer simulation of a modified Lebwohl-Lasher model is presented. The model consists of a set of interaction centres placed at the sites of a cubic lattice. The angular part of the pair potential is a second Legendre polynomial of the relative orientation between the two particles, like that of the Lebwohl-Lasher model. Each particle interacts with its six nearest neighbours with an attractive anisotropic potential differing in strength for the four horizontal and the two vertical neighbours. Various values of the in-plane to out-of-plane coupling ratio δ have been considered, i.e. δ = 0.75, 0.5, 0.1, 0.0. The latter case corresponds to the limiting situation of a two-dimensional lattice. Systems with a 1000 particles have been simulated for δ = 0.75, 0.5 and 0.1 while a sample of 3600 particles has been investigated for the two-dimensional lattice. Comparisons are made with available simulations and with mean field theory. We find that the molecular field theory predictions worsen as the effective coordination number is decreased. Energy, specific heat, second and fourth rank order parameters have been evaluated for the various models. We also present, for the first time, a way of approximately reconstructing the pair distribution, G(r₁₂, ω₁₂), using maximum entropy and second and fourth rank two particle order parameters.