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
where , is the angle between the axes of nearest neighbour particles and , and is a second order Legendre polynomial.
Planar Lebwohl–Lasher model
The planar Lebwohl-Lasher appears when the lattice considered is two-dimensional. The square lattice is the usual choice for most of the simulation studies. This system exhibits a continuous transition. The ascription of such a transition to the Kosterlitz-Touless type is still under discussion    .
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 .
- 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)
- N. V. Priezjev and Robert A. Pelcovits Cluster Monte Carlo simulations of the nematic-isotropic transition Phys. Rev. E 63, 062702 (2001) [4 pages]
- Zhengping Zhang, Ole G. Mouritsen, and Martin J. Zuckermann, "Weak first-order orientational transition in the Lebwohl-Lasher model for liquid crystals", Physical Review Letters 69 pp. 2803-2806 (1992)
- Raj Shekhar, Jonathan K. Whitmer, Rohit Malshe, J. A. Moreno-Razo, Tyler F. Roberts, and Juan J. de Pablo "Isotropic–nematic phase transition in the Lebwohl–Lasher model from density of states simulations", Journal of Chemical Physics 136 234503 (2012)
- Douglas J. Cleaver and Michael P. Allen, " Computer simulation of liquid crystal films", Molecular Physics 80 pp 253-276 (1993)
- 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", Physica A 148 pp. 298-311 (1988)
- H. Kunz, and G. Zumbach "Topological phase transition in a two-dimensional nematic n-vector model: A numerical study" Physical Review B 46, 662-673 (1992)
- Ricardo Paredes V., Ana Isabel Fariñas-Sánchez, and Robert Botet "No quasi-long-range order in a two-dimensional liquid crystal", Physical Review E 78, 051706 (2008)
- Martin A. Bates "Computer simulation study of the phase behavior of a nematogenic lattice-gas model", Physical Review E 64 051702 (2001)