COMPUTER SIMULATION STUDY OF A NEMATOGENIC LATTICE-GAS MODEL

Abstract

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 [Formula: see text] here P2(τ) denotes the second Legendre polynomial, νj=0,1 are occupation numbers, uj are the unit vectors (classical spins), and ∊ is a positive quantity setting energy and temperature scales (i.e. T*=k B T/∊); the total Hamiltonian is given by [Formula: see text] where ∑{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 μ0<0, such that, for all μ>μ0, the system supports an ordering transition at a finite, μ-dependent, temperature. We have studied here the case μ=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.