Absence of Neel order in Heisenberg chains: Long-range antiferromagnetic interactions

We have studied the Heisenberg chain with long-range antiferromagnetic interactions proportional to (-1)(n)/n(p) (n=1,2,...,infinity) by the method of a double-time-temperature Green's function within Tyablikov's decoupling approximation. Using the two-sublattice approach developed by Hewson and ter Haar, and solving the equation of motion for the Green's function, we obtain the Neel temperature T-N as a function of p. We have conjectured that for all p>1 the present approach predicts orientational disorder at all finite temperatures (i.e., T-N=0). Our results are in accordance with spin-wave arguments and disagreement with renormalization group that predicts a phase transition at psimilar or equal to1.85 at T=0.