Lebwohl-Lasher model

The Lebwohl-Lasher model is a lattice version of the Maier-Saupe mean field model of a nematic liquid crystal. The Lebwohl-Lasher model consists of a cubic lattice with the pair potential

${\mathrm{\Phi }}_{ij}=-{ϵ}_{ij}{P}_2(\cos {\beta }_{ij})$

where ${ϵ}_{ij}>0$, ${\beta }_{ij}$ is the angle between nearest neighbour particles $i$ and $j$, and $P_2$ is a second order Legendre polynomial.

Isotropic-nematic transition

(Ref. 3)

$T_{N{I}^{*}}^{*}=\frac{k_B{T}_{NI}}{ϵ}=1.1201\pm 0.0006$

References

1. P. A. Lebwohl and G. Lasher "Nematic-Liquid-Crystal Order—A Monte Carlo Calculation", Physical Review A 6 pp. 426 - 429 (1972)
   1. Erratum, Physical Review A 7 p. 2222 (1973)
2. U. Fabbri and C. Zannoni "A Monte Carlo investigation of the Lebwohl-Lasher lattice model in the vicinity of its orientational phase transition", Molecular Physics pp. 763-788 58 (1986)