COMPUTER-SIMULATION STUDY OF A 2-DIMENSIONAL NEMATOGENIC LATTICE MODEL WITH LONG-RANGE INTERACTIONS ISOTROPIC IN SPIN SPACE

We have considered a classical spin system, consisting of n-component unit vectors (n = 2, 3) {u(k), k is an element of Z(d))}, associated w ith a d-dimensional lattice Z(d), d = 1, 2, and interacting via pair p otentials, isotropic in spin space, and of the long-range form [GRAPHI CS] Here epsilon is a positive constant setting energy and temperature scales (i.e. T = k(B)T/epsilon)) and x(k) denotes dimensionless latt ice-site coordinates. Extending previous rigorous results, one can pro ve the existence of an ordering transition at finite temperature when 0 < sigma < d, and its absence when sigma greater than or equal to d. We have studied the case defined by n = 3, d = 2, sigma = 1, by means of computer simulation, Molecular Field and Two-Site Cluster theory. T he Two-Site Cluster approach was found to bring about a recognizable i mprovement over Molecular Field; on the other hand, comparison with th e Lebwohl-Lasher lattice model shows that the long-range character of the interaction tends to increase the transition temperature towards i ts Molecular Field limit.