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

We have considered a classical spin system, consisting of 3-component unit vectors, associated with a one-dimensional lattice (uk, Ic is an element of Z), and interacting via translationally invariant pair potentials, isotropic in spin space, and of the long-range form W = W-jk = -epsilon\j - k\P--1-sigma(2)(tau), tau = tau(jk) = u(j) . u(k), sigma > O, where epsilon is a positive constant setting energy and temperature scales (i.e. T* = k(B)T/epsilon). Extending previous rigorous results, one can prove the existence of an ordering transition at finite temperature when 0 < sigma < 1, and its absence when sigma greater than or equal to 1. We have studied the border case sigma = 1, by means of computer simulation. Similarly to the magnetic counterparts of the present model, we found evidence suggesting a transition to a low-temperature phase with slow decay of correlations and infinite susceptibility, i.e. a Berezhinskii-Kosterlitz-Thouless-like transition; the transition temperature was estimated to be Theta = 0.475 +/- 0.005.