COMPUTER SIMULATION STUDY OF A NEMATOGENIC LATTICE-GAS MODEL WITH FOURTH-RANK INTERACTIONS

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 nearestneighboring sites interact via the nematogenic potential [Formula: see text] here P4(τ) denotes the fourth Legendre polynomial, nuj=0,1 are occupation numbers, uj are unit vectors (classical spins), and ∊ is a positive quantity setting the 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-neighboring pairs of lattice sites. The saturated-lattice version of this model defines a nematogenic lattice model, already studied in the literature, and found to possess a transition to an orientationally ordered phase at low temperature; moreover, 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 present here a detailed study of the case μ=0, and characterize it by means of Monte Carlo simulation, Mean Field and Two Site Cluster treatments; the latter significantly improves the agreement with simulation results.