Computer simulation study of a simple cubatic mesogenic lattice model.

Over the last , the possible existence of a cubatic mesophase, possessing cubic orientational order (i.e., along three mutually orthogonal axes) but no translational one, has been addressed theoretically, and predicted in some cases, where the investigated interaction models involved hard-core repulsion only; on the other hand, no experimental realizations of such a phase are known at the time being. The present paper addresses a very simple cubatic mesogenic lattice model, involving continuous interactions; we consider particles possessing Oh symmetry, whose centers of mass are associated with a three-dimensional simple-cubic lattice; the pair potential is taken to be isotropic in orientation space, and restricted to nearest neighboring sites; let the two orthonormal triads {uj, j=1, 2, 3} and {vk, k=1, 2, 3} define orientations of a pair of interacting particles, and let fjk=vj.uk. The interaction model studied here is defined by the simplest nontrivial (quartic) polynomial in the scalar products f jk, consistent with the assumed symmetry and favoring orientational order; it is, so to speak, the cubatic counterpart of the Lebwohl-Lasher model for uniaxial nematics. The model was investigated by mean field theory and Monte Carlo simulation, and found to produce a low-temperature cubatically ordered phase, undergoing a first order transition to the isotropic phase at higher temperature; the mean field treatment yielded results in reasonable qualitative agreement with simulation.