Editing Lebwohl-Lasher model
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The Lebwohl–Lasher model consists of a cubic lattice occupied by uniaxial [[Nematic phase|nematogenic]] particles with the [[Intermolecular pair potential | pair potential]] | The Lebwohl–Lasher model consists of a cubic lattice occupied by uniaxial [[Nematic phase|nematogenic]] particles with the [[Intermolecular pair potential | pair potential]] | ||
:<math>\Phi_{ij} = -\ | :<math>\Phi_{ij} = -\epsilon_{ij} P_2 (\cos \beta_{ij}) </math> | ||
where <math>\ | where <math>\epsilon_{ij} > 0</math>, <math>\beta_{ij}</math> is the angle between the axes of nearest neighbour particles <math>i</math> and <math>j</math>, and <math>P_2</math> is a second order [[Legendre polynomials |Legendre polynomial]]. | ||
==Isotropic-nematic transition== | ==Isotropic-nematic transition== | ||
Fabbri and Zannoni estimated the transition temperature <ref>[http://dx.doi.org/10.1080/00268978600101561 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)]</ref> via a [[Monte Carlo]] simulation: | Fabbri and Zannoni estimated the transition temperature <ref>[http://dx.doi.org/10.1080/00268978600101561 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)]</ref> via a [[Monte Carlo]] simulation: |