# Lebwohl-Lasher model

The Lebwohl-Lasher model is a lattice version of the Maier-Saupe mean field model of a nematic liquid crystal [1][2]. The Lebwohl-Lasher model consists of a cubic lattice occupied by uniaxial nematogenic particles with the pair potential

$\Phi_{ij} = -\epsilon P_2 (\cos \beta_{ij})$

where $$\epsilon > 0$$, $$\beta_{ij}$$ 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 [3] via a Monte Carlo simulation:

$T^*_{NI}= \frac{k_BT_{NI}}{\epsilon}=1.1232 \pm 0.0006$

More recently N. V. Priezjev and Robert A. Pelcovits [4] used a Monte Carlo cluster algorithm and obtained:

$T^*_{NI}= \frac{k_BT_{NI}}{\epsilon}=1.1225 \pm 0.0001$

See also the paper by Zhang et al. [5] and that of Shekhar et al. [6].

## Confined systems

The Lebwohl-Lasher model has been used to study the effect of confinement in the phase behavior of nematogens [7]

## Planar Lebwohl–Lasher model

The planar Lebwohl-Lasher appears when the lattice considered is two-dimensional. The square lattice is the usual choice for most of the simulation studies. This system exhibits a continuous transition. The ascription of such a transition to the Kosterlitz-Touless type is still under discussion [8] [9] [10] [11].

## 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 [12].