We have considered a nematogenic lattice model, consisting of three-component unit vectors, associated with a two-dimensional lattice, and interacting via London–Heller–de Boer dispersion potential restricted to nearest neighbours, already studied by simulation in three dimensions (Mol. Phys. 42 (1981) 1205; Int. J. Mod. Phys. B 13 (1999) 3879; Phys. Rev. E 65 (2002) 041706). The model is defined byΔjk=ε[(γ2−γ)Sjk+γ2(−32hjk+1)],wherehjk=(3ajak−τjk)2,Sjk=P2(aj)+P2(ak),r=xj−xk,s=r/|r|,aj=uj·s,ak=uk·s,τjk=uj·ukandᾱ=13(α||+2α⊥),γ=α||−α⊥3ᾱ.Here the two-component vectors xj∈Z2 define centre-of-mass coordinates of the particles, and uk are three-component unit vectors defining their orientations; α||,α⊥ are the eigenvalues of the molecular polarizability tensor, γ denotes its relative anisotropy, and ε is a positive quantity setting energy and temperature scales (i.e., T∗=kBT/ε). In two dimensions, and in contrast to the Lebwohl–Lasher lattice model, the potential's anisotropic character does not prevent existence of orientational order at finite temperature. Monte Carlo calculations were carried out using the two values γ=±12, and comparisons are reported with a mean field (MF) treatment as well. In both cases, some orientational order was found to survive up to temperatures well above the disordering transition of the three-dimensional counterpart, possibly at all finite temperatures.
