https://en.wikipedia.org/wiki/Soft_matter
https://en.wikipedia.org/wiki/Liquid_crystal
Liquid crystals (LC) are a state of matter which has properties between
those of conventional liquids and those of solid crystals.
For instance, a liquid crystal may flow like a liquid, but its molecules
may be oriented in a crystal-like way.
LC molecules are similar to rods or discs.
There are many different types of liquid-crystal phases:
nematic LC (orientational order only),
smectic LC (2D crystals),
columnar phases (1D crystals), etc.
LC systems are studied in 'soft matter physics', a subfield of 'condensed matter physics'.
increasing temperature → crystal | liquid | gas # not LC material (H2O) crystal | smectic | nematic | isotropic liquid | gas # thermotropic LC material '|' denotes a phase transition.
http://www.sklogwiki.org/SklogWiki/index.php/Lebwohl-Lasher_model
The Lebwohl-Lasher model is a lattice version of the Maier-Saupe mean field model of a nematic liquid crystal. A cubic lattice is occupied by uniaxial nematogenic particles with the pair potential H_ij.
H_ij = -ε P_2(cos θ_ij),
where ε > 0,
θ_ij is the angle between the axes of nearest neighbour particles i and j,
and P_2(x) = (3x^2-1)/2 is a second order Legendre polynomial.
For parallel particles H_ij = -ε P_2(1) = -ε.
Note that vectors \vec{n} and -\vec{n} describe the same particle orientation.
[1971 Straley] [1985 Frenkel Eppenga]
Square lattice 2D, vectors \vec{n} in the 2D orientational space,
periodic boundary conditions.
The existence of the true phase transition is discussed in the literature.
Cubic lattice 3D, vectors \vec{n} in 3D orientational space,
periodic boundary conditions.
The estimated isotropic-nematic transition temperature
T_NI = 1.1232(6) [1986 Fabbri Zannoni] 30x30x30 cubic lattice