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

Abstract

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 ($\beta >{\beta }_c(\mu )$).

11 pages

Cited by in corpus (2)

• First order phase transitions in classical lattice gas spin models
• Nematic first order phase transition for liquid crystals in the van der Waals-Kac limit