Computer simulation study of a nematogenic lattice-gas model

We have considered a classical lattice-gas model, consisting of a three-dimensional simple-cubic lattice, whose sites host three-component unit vectors; pairs of nearest-neighbouring sites interact via the nematogenic potential Psi(jk) = -epsilon nu(j)nu(k)P(2)(tau), tau = tau(jk) = u(j) . u(k), here P-2(tau) denotes the second Legendre polynomial, nu(j) = 0, 1 are occupation numbers, u(j) are the unit vectors (classical spins), and epsilon is a positive quantity setting energy and temperature scales (i.e. T* = k(B)T/epsilon); the total Hamiltonian is given by [GRAPHICS] where Sigma({j<k}) denotes sum over all distinct nearest-neighbouring pairs of lattice sites. The saturated-lattice version of this model defines the extensively studied Lebwohl-Lasher model, possessing a transition to an orientationally ordered phase at low temperature; according to available rigorous results, there exists a mu(0) < 0, such that, for all mu > mu(0), the system supports an ordering transition at a finite, mu-dependent, temperature. We have studied here the case mu = 0, and found evidence of a transition, taking place at a lower temperature, and possessing a more pronounced first-order character than its Lebwohl-Lasher counterpart; a Mean Field treatment has also been worked out, and found to yield results in qualitative agreement with simulation.