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

Abstract

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 <P ₂>, <P ₄> have been calculated and a new algorithm is proposed for the computation of <P ₄>. 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.