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 occupied by uniaxial nematogenic particles with the pair potential

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

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

Isotropic-nematic transition

Fabbri and Zannoni estimated the transition temperature via a Monte Carlo simulation:

$T_{NI}^{*}=\frac{k_B{T}_{NI}}{ϵ}=1.1232\pm 0.0006$

More recently N. V. Priezjev and Robert A. Pelcovits used a Monte Carlo cluster algorithm and obtained:

$T_{NI}^{*}=\frac{k_B{T}_{NI}}{ϵ}=1.1225\pm 0.0001$

See also the paper by Zhang et al. .

Planar Lebwohl–Lasher model

The planar Lebwohl-Lasher appears when the lattice considered is two-dimensional. This system exhibits a continuous transition. The ascription of such a transition to the Kosterlitz-Touless type is still under discussion .

Lattice Gas Lebwohl-Lasher model

This model is the lattice gas version of the Lebwohl-Lasher model. In this case the sites of the lattice can be occupied by particles or empty. The interaction between nearest-neighbour particles is that of the Lebwohl-Lasher model. This model has been studied in .