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

$\Phi _{ij}=-\epsilon _{ij}P_{2}(\cos \beta _{ij})$

where $\epsilon _{ij}>0$, $\beta _{ij}$ is the angle between nearest neighbour particles $i$ and $j$, and $P_{2}$ is a second order Legendre polynomial.

Isotropic-nematic transition

(Ref. 3)

$T_{NI^{*}}^{*}={\frac {k_{B}T_{NI}}{\epsilon }}=1.1201\pm 0.0006$

Planar Lebwohl–Lasher model

The planar Lebwohl-Lasher appears when the lattice considered is two-dimensional. This system exhibits a Kosterlitz-Touless continuous transition. (Mondal, Roy; Physics Letters A, 2003, 312, 397-410) (Chiccoli, C.; Pasini, P. & Zannoni, C., Physica, 1988, 148A, 298-311)

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)