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 $\epsilon _{ij}>0$, Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \beta_{ij}} is the angle between the axes of nearest neighbour particles Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle i} and Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle j} , and Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle P_2} is a second order Legendre polynomial.

Isotropic-nematic transition

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

Planar Lebwohl–Lasher model

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

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 .