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

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where 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 \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 $P_{2}$ is a second order Legendre polynomial.

Isotropic-nematic transition

(Ref. 3)

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Planar Lebwohl–Lasher model

The planar Lebwohl-Lasher appears when the lattice considered is two-dimensional. This system exhibits a Kosterlitz-Touless continuous transition. (Mondal, Roy; Physics Letters A, 2003, 312, 397-410) (Chiccoli, C.; Pasini, P. & Zannoni, C., Physica, 1988, 148A, 298-311)

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-neighbor particles is that of the Lebwohl-Lasher model. This model has been studied in

Bates, M. A., Computer simulation study of the phase behavior of a nematogenic lattice-gas model, Phys. Rev. E, 2001, 64, 051702

References

1. P. A. Lebwohl and G. Lasher "Nematic-Liquid-Crystal Order—A Monte Carlo Calculation", Physical Review A 6 pp. 426 - 429 (1972)
   1. Erratum, Physical Review A 7 p. 2222 (1973)
2. 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)