A Monte Carlo investigation of the Lebwohl-Lasher lattice model in the vicinity of its orientational phase transition

The Lebwohl-Lasher model of nematogens consists of a system of particles placed at the sites of a cubic lattice and interacting with a pair potential U i,j = -ϵ ij P 2(cos β ij ), where ϵ ij is a positive constant, ϵ, for nearest neighbours particles i and j and β ij is the angle between the axis of these two molecules. We have investigated this model using Monte Carlo simulations with periodic boundary conditions on a 30 × 30 × 30 lattice while the largest system previously studied was 20 × 20 × 20. The number of simulation runs near the transition is also significantly higher than in previous simulations to allow a more precise determination of the orientational transition temperature T * NI. The transition temperature has been placed at kT/ϵ = 1·1232 ± 0·0006, refining previous estimates. Orientational order parameters , have been calculated and a new algorithm is proposed for the computation of . Particular attention has been devoted to pretransitional properties. Pair correlations G 2(r), G 4(r) as well as the second rank g 2-factor are reported. g 2 is found to diverge at a temperature T * NI* = kT/ϵ = 1·1201 ± 0·0006 and to fit the Landau-de Gennes behaviour except near the transition. Our results indicate therefore that the Lebwohl-Lasher model can yield the small difference between the nematic-isotropic transition temperature and the isotropic phase limiting instability temperature without the need of introducing additional terms in the potential.