Lebwohl-Lasher model

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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

Fabbri and Zannoni estimated the transition temperature [3] using Monte Carlo simulation:

More recently N. V. Priezjev and Robert A. Pelcovits [4] used a Monte Carlo cluster algorithm and obtained:

See also the paper by Zhang et al. [5]

Planar Lebwohl–Lasher model

The planar Lebwohl-Lasher appears when the lattice considered is two-dimensional. This system exhibits a continuous transition. The ascription of such a transition to the Kosterlitz-Touless type is still under discussion [6] [7] [8] [9].

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 [10].

References