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

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

where $\epsilon _{ij}>0$, $\beta _{ij}$ 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 using Monte Carlo simulation:

$T_{NI}^{*}={\frac {k_{B}T_{NI}}{\epsilon }}=1.1232\pm 0.0006$

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

$T_{NI}^{*}={\frac {k_{B}T_{NI}}{\epsilon }}=1.1225\pm 0.0001$

Planar Lebwohl–Lasher model

The planar Lebwohl-Lasher appears when the lattice considered is two-dimensional. This system exhibits a Kosterlitz-Touless continuous transition .

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 .