MEAN FIELD, TWO-SITE CLUSTER, AND 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 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. Continuing along the lines of our previous communication [S. Romano, Int. J. Mod. Phys.B14, 1195 (2000)], we present here a detailed study of the case μ = 0, using Monte Carlo simulation, Mean Field and Two Site Cluster treatments; the latter significantly improves the agreement with simulation results.