On Long-Range Order in Low-Dimensional Lattice-Gas Models of Nematic Liquid Crystals

Details On Long-Range Order in Low-Dimensional Lattice-Gas Models of Nematic Liquid Crystals On Long-Range Order in Low-Dimensional Lattice-Gas Models of Nematic Liquid Crystals

1994-11-08

arxiv.org/abs/cond-mat/9411033v1

Physics

Condensed Matter

11 pages

Scientific paper

10.1016/0375-9601(95)00204-G

The problem of the orientational ordering transition for lattice-gas models of liquid crystals is discussed in the low-dimensional case $d=1,2$. For isotropic short-range interactions, orientational long-range order at finite temperature is excluded for any packing of molecules on the lattice $Z^d$; on the other hand, for reflection-positive long-range isotropic interactions, we prove existence of an orientational ordering transition for high packing ($\mu > \mu_0$) and low temperatures ($\beta > \beta_c(\mu)$).

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