  In contrast to thermotropic biaxial nematic phases, for which some long
sought for experimental realizations have been obtained, no experimental
realizations are yet known for their tetrahedratic and cubatic
counterparts,involving orientational orders of ranks 3 and 4, respectively,
also studied theoretically over the last few decades. In previous studies,
cubatic order has been found for hard-core or continuous models consisting of
particles possessing cubic or nearly-cubic tetragonal or orthorhombic
symmetries; in a few cases, hard-core models involving uniaxial ($D_{\infty
h}-$symmetric) particles have been claimed to produce cubatic order as well.
Here we address by Monte Carlo simulation a lattice model consisting of
uniaxial particles coupled by long-range dispersion interactions of the
London-De Boer-Heller type; the model was found to produce no second-rank
nematic but only fourth-rank cubatic order, in contrast to the nematic behavior
long known for its counterpart with interactions truncated at nearest-neighbor
separation.
