Lebwohl-Lasher model: Difference between revisions

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m (stub removed)
m (→‎Isotropic-nematic transition: correction (I hope) of the transition temperature)
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<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>
<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>


:<math>T^*_{NI}= \frac{k_BT_{NI}}{\epsilon}=1.1201 \pm 0.0006</math>
:<math>T^*_{NI}= \frac{k_BT_{NI}}{\epsilon}=1.1232 \pm 0.0006</math>


==Planar Lebwohl–Lasher model ==
==Planar Lebwohl–Lasher model ==

Revision as of 16:14, 20 February 2009

The Lebwohl-Lasher model is a lattice version of the Maier-Saupe mean field model of a nematic liquid crystal [1][2]. 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.

Isotropic-nematic transition

[3]

Planar Lebwohl–Lasher model

The planar Lebwohl-Lasher appears when the lattice considered is two-dimensional. This system exhibits a Kosterlitz-Touless continuous transition [4] [5].

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 [6].

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. Erratum, 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)
  4. Mondal, Roy; Physics Letters A, 2003, 312, 397-410
  5. Chiccoli, C.; Pasini, P. & Zannoni, C., Physica, 1988, 148A, 298-311
  6. Bates, M. A., Computer simulation study of the phase behavior of a nematogenic lattice-gas model, Phys. Rev. E, 2001, 64, 051702