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

Abstract

We have considered a classical spin system, consisting of n-component unit vectors (n = 2, 3) {uk, k∈Zd}, associated with a d-dimensional lattice Zd, d=1, 2, and interacting via pair potentials, isotropic in spin space, and of the long-range form [Formula: see text] Here ∊ is a positive constant setting energy and temperature scales (i.e. T*=kBT/∈), and xk denotes dimensionless lattice-site coordinates. Extending previous rigorous results, one can prove the existence of an ordering transition at finite temperature when 0<σ< d, and its absence when σ≥d. We have studied the case defined by n=3, d=2, σ=1, by means of computer simulation, Molecular Field and Two-Site Cluster theory. The Two-Site Cluster approach was found to bring about a recognizable improvement over Molecular Field; on the other hand, comparison with the Lebwohl-Lasher lattice model shows that the long-range character of the interaction tends to increase the transition temperature towards its Molecular Field limit.