Monte Carlo simulation of disordered one dimensional systems with long range antiferromagnetic interactions

Abstract

We consider a classical system, consisting of m-component unit vectors (m = 2 and 3), associated with a one dimensional lattice {u^k/k ε Z} and interacting via translationally and rotationally invariant pair potentials of the form

The system has been proven rigorously to possess an orientationally ordered phase stable at low but finite temperature when c = −1, 1 < p < 2, and to disorder at all finite temperatures for c = ± 1 and p ≧ 2. This theorem also holds for the corresponding spherical model, whereas, in the Ising model, the ordered phase survives for 1 < p ≦ 2. We report here Monte Carlo simulation results for the antiferromagnetic models defined by c = + 1,p = 2, m = 2 and 3. Comparison with their exactly soluble nearest neighbour counterparts shows that the long range antiferromagnetic interaction significantly weakens finite range correlations; this effect is more pronounced for m = 3 than for 2.