Computer simulation study of a two-dimensional nematogenic lattice model based on a mapping from elastic free-energy density

Over the last few years, it has been recognized that on can construct, in different ways, a nematogenic lattice model with pairwise additive interactions, which approximately reproduce the elastic free energy density, and where the parameters defining the pair potential are expressed in terms of elastic constants. An anisotropic nematogenic pair interaction of this kind, originally proposed by Gruhn and Hess [Z. Naturforsch. A 51 (1996) 1] has been investigated by Monte Carlo simulation, for particle centers of mass associated with both a three- and a two-dimensional lattice. Another approximate procedure for the mapping had also been proposed, and studied by simulation on a three-dimensional lattice (Luckhurst and Romano [Liq. Cryst. 26 (1999) 871]) continuing along this line, we investigate here the 2-dimensional lattice counterpart, by means of Mean Field theory and Monte Carlo simulations. In 2 dimensions, the anisotropic character of these potential models does not preclude the existence of orientational order at finite temperature. The model produces a ground state where particles are aligned in the lattice plane; both Mean Field (MF) predictions and simulation results for the second-rank ordering tensor show a low-temperature régime where the system becomes biaxial, with the main director aligned along a lattice axis; at higher temperature there is a transition to uniaxial order with negative order parameter, and director orthogonal to the lattice plane; this orientational order survives up to temperatures higher than the transition temperature of the 3-dimensional counterpart, possibly at all finite temperatures. MF predictions and simulation results appear to agree qualitatively, but in quantitative terms the MF prediction for the transition temperature is some 56% too high.