Lebwohl-Lasher model: Difference between revisions
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==Planar Lebwohl–Lasher model == | ==Planar Lebwohl–Lasher model == | ||
The planar Lebwohl-Lasher appears when the lattice considered is two-dimensional. | The planar Lebwohl-Lasher appears when the lattice considered is two-dimensional. | ||
This system exhibits a [[Kosterlitz-Thouless transition|Kosterlitz-Touless]] continuous transition | This system exhibits a [[Kosterlitz-Thouless transition|Kosterlitz-Touless]] continuous transition | ||
<ref>Mondal, | <ref>[http://dx.doi.org/10.1016/S0375-9601(03)00576-0 Enakshi Mondal and Soumen Kumar Roy "Finite size scaling in the planar Lebwohl–Lasher model", Physics Letters A '''312''' pp. 397-410 (2003)]</ref> | ||
<ref>Chiccoli, | <ref>[http://dx.doi.org/10.1016/0378-4371(88)90148-3 C. Chiccoli, P. Pasini, and C. Zannoni "A Monte Carlo investigation of the planar Lebwohl-Lasher lattice model", ĥysica A '''148''' pp. 298-311 (1988)]</ref>. | ||
==Lattice Gas Lebwohl-Lasher model== | ==Lattice Gas Lebwohl-Lasher model== | ||
This model is the lattice gas version of the Lebwohl-Lasher model. In this case | 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 | 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. | between nearest-neighbour particles is that of the Lebwohl-Lasher model. | ||
This model has been studied in | This model has been studied in | ||
<ref> | <ref>[http://dx.doi.org/10.1103/PhysRevE.64.051702 Martin A. Bates "Computer simulation study of the phase behavior of a nematogenic lattice-gas model", Physical Review E '''64''' 051702 (2001)]</ref>. | ||
==References== | ==References== | ||
<references/> | <references/> | ||
[[category: models]] | [[category: models]] | ||
[[category: liquid crystals]] | [[category: liquid crystals]] | ||
Revision as of 12:44, 23 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
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
- ↑ P. A. Lebwohl and G. Lasher "Nematic-Liquid-Crystal Order—A Monte Carlo Calculation", Physical Review A 6 pp. 426 - 429 (1972)
- ↑ Erratum, Physical Review A 7 p. 2222 (1973)
- ↑ 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)
- ↑ Enakshi Mondal and Soumen Kumar Roy "Finite size scaling in the planar Lebwohl–Lasher model", Physics Letters A 312 pp. 397-410 (2003)
- ↑ C. Chiccoli, P. Pasini, and C. Zannoni "A Monte Carlo investigation of the planar Lebwohl-Lasher lattice model", ĥysica A 148 pp. 298-311 (1988)
- ↑ Martin A. Bates "Computer simulation study of the phase behavior of a nematogenic lattice-gas model", Physical Review E 64 051702 (2001)