Zp. Zhang et al., PHASE-TRANSITION AND DIRECTOR FLUCTUATIONS IN THE 3-DIMENSIONAL LEBWOHL-LASHER MODEL OF LIQUID-CRYSTALS, Molecular physics, 80(5), 1993, pp. 1195-1221
Monte Carlo computer simulation techniques are used to study the orien
tational phase transition in the three-dimensional Lebwohl-Lasher mode
l which couples molecular rotors placed on a cubic lattice by the pote
ntial P-2(cos theta(ij)). The orientational transition is a model of t
he nematic-isotropic phase transition in liquid crystals. The simulati
ons involve the determination of energy and order parameter distributi
on functions which permit free energy functions to be derived. The dat
a have been analysed by finite size scaling methods to reveal the natu
re of the phase transition which is found to be weakly first order wit
h stability limits of the nematic and isotropic phases being extremely
close to the equilibrium transition temperature, in good agreement wi
th experimental studies of room temperature nematogens. Results are re
ported for the specific heat, the axial and biaxial susceptibilities,
as well as the enthalpy and nematic order parameter discontinuity at t
he transition. It is shown that the inclusion of a term P-4(cos theta(
ij)) in the potential enhances the first-order character of the transi
tion and displaces the stability limits further from the equilibrium t
ransition temperature. The director fluctuations have been analysed, a
nd it is found that, whereas the fluctuations in the isotropic phase f
ollow ordinary Brownian motion, the fluctuations in the nematic phase
correspond to fractional Brownian motion. By introducing a symmetry-br
eaking field, -h(2)cos theta(i)(2):, a field-induced crossover between
fractional and normal Brownian motion is observed in agreement with r
ecent neutron scattering studies on deuterated p-azoxyanisole.