Lebwohl-Lasher model: Difference between revisions

From SklogWiki
Jump to navigation Jump to search
(→‎Isotropic-nematic transition: another estimation from the literature)
Line 11: Line 11:
:<math>T^*_{NI}= \frac{k_BT_{NI}}{\epsilon}=1.1232 \pm 0.0006</math>
:<math>T^*_{NI}= \frac{k_BT_{NI}}{\epsilon}=1.1232 \pm 0.0006</math>


More recently N. V. Priezjev and Robert A. Pelcovits <ref>[http://dx.doi.org/10.1103/PhysRevE.63.062702  
More recently N. V. Priezjev and Robert A. Pelcovits <ref>[http://dx.doi.org/10.1103/PhysRevE.63.062702 N. V. Priezjev and Robert A. Pelcovits ''Cluster Monte Carlo simulations of the nematic-isotropic transition'' Phys. Rev. E 63, 062702 (2001) [4 pages]] </ref> used a Monte Carlo [[cluster algorithms|cluster algorithm]] and got:
''Cluster Monte Carlo simulations of the nematic-isotropic transition'' Phys. Rev. E 63, 062702 (2001) [4 pages]
]</ref> used a Monte Carlo [[cluster algorithms|cluster algorithm]] and got:


:<math>T^*_{NI}= \frac{k_BT_{NI}}{\epsilon}=1.1225 \pm 0.0001 </math>
:<math>T^*_{NI}= \frac{k_BT_{NI}}{\epsilon}=1.1225 \pm 0.0001 </math>

Revision as of 19:43, 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

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 got:

Planar Lebwohl–Lasher model

The planar Lebwohl-Lasher appears when the lattice considered is two-dimensional. This system exhibits a Kosterlitz-Touless continuous transition [5] [6].

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 [7].

References