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
where , is the angle between the axes of nearest neighbour particles and , and is a second order Legendre polynomial.
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    .
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 .
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