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 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 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

(Ref. 3)

$T_{NI^{*}}^{*}={\frac {k_{B}T_{NI}}{\epsilon }}=1.1201\pm 0.0006$

References

1. P. A. Lebwohl and G. Lasher "Nematic-Liquid-Crystal Order—A Monte Carlo Calculation", Physical Review A 6 pp. 426 - 429 (1972)
2. P. A. Lebwohl and G. Lasher "Nematic-Liquid-Crystal Order-A Monte Carlo Calculation", Physical Review A 7 p. 2222 (1973)
3. U. Fabbri and C. Zannoni "A Monte Carlo investigation of the Lebwohl-Lasher lattice model in the vicinity of its orientational phase transition", Molecular Physics pp. 763-788 58 (1986)