COMPUTER SIMULATION STUDY OF A NEMATOGENIC LATTICE-GAS MODEL BASED ON THE NEHRING–SAUPE INTERACTION POTENTIAL

Abstract

Over 25 years ago, Nehring and Saupe proposed an anisotropic nematogenic lattice model, whose restriction to nearest neighbours has the form [Formula: see text] Here the three-component vectors xj∈Z3define centre-of-mass coordinates of the particles, and ukare three-component unit vectors defining their orientations; ∊ is a positive quantity setting energy and temperature scales (i.e. T*=kBT/∊); this model is seen to be the anisotropic counterpart to the generic Lebwohl–Lasher lattice model. It has often been used for approximate calculations of elastic properties, and has recently been studied by simulation [Hashim and Romano, Int. J. Mod. Phys.B13, 3879 (1999)]. We study here its lattice-gas extension, whose Hamiltonian is defined by [Formula: see text] where νk=0,1 denote occupation numbers, ∑{j<k}denotes sum over all distinct nearest-neighbouring pairs of lattice sites, and μ is the chemical potential. The model has been addressed by Monte Carlo simulation; comparisons are reported with Mean Field theory as well as with the Lebwohl–Lasher counterpart.