ON LONG-RANGE ORDER IN LOW-DIMENSIONAL LATTICE-GAS MODELS OF NEMATIC LIQUID-CRYSTALS

The problem of the orientational ordering transition for lattice-gas m odels 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-r ange isotropic interactions, we prove the existence of an orientationa l ordering transition for high packing (mu > mu(0)) and low temperatur es (beta > beta(c)(mu)).