Computer simulation study of a two-dimensional nematogenic lattice model based on the Nehring-Saupe interaction potential

We have considered a nematogenic lattice model, consisting of 3-component unit vectors, associated with a 2-dimensional lattice, and interacting via the nearest-neighbour potential model proposed by Nehring and Saupe [Int. J. Mod. Phys. 54 (1971) 337], and already studied by simulation in 3 dimensions [Int. J. Mod. Phys. 13 (1999) 3879; Mod. Phys. Lett. B 15 (2001) 137]. The model is defined by psi(jk) = epsilon[-3/2(3a(j)a(k) - tau(jk))(2) + 1], r = x(j) - x(k), s = r/\r\, a(j) = u(j)(.)s, a(k) = u(k)(.)s, tau(jk) = u(j)(.)u(k). Here the 2-component vectors x(j) is an element of Z(2) define centre-of-mass coordinates of the particles, and u(k) are three-component unit vectors defining their orientations; c is a positive quantity setting energy and temperature scales (i.e., T* = k(B) T/epsilon); this model can be regarded as the anisotropic counterpart to the generic Lebwohl-Lasher lattice model; in 2 dimensions, its anisotropic character does not preclude the existence of orientational order at finite temperature. The model produces a ground state where particles are aligned along a lattice axis; both Mean Field (MF) predictions and simulation results for the second-rank ordering tensor show a low-temperature regime 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 45% too high. (C) 2002 Elsevier Science B.V. All rights reserved.