Parreira J. R., Bolina O., Perez J. F.
Neel Order in the Ground State of Heisenberg Antiferromagnetic
chains with Long Range Interactions
(15K, LaTeX)

ABSTRACT.  We consider the ground state of one-dimensional antiferromagnets with 
long range interactions with Hamiltonian given by
$$
H=\sum_{x} \sum_{n} (-1)^{n} J(n) {\bf S}_{x}.{\bf S}_{x+n}
$$
where $J(n)=n^{-\alpha}$, with $J>0$. We prove N\'eel order for all 
$1<\alpha<3$ if the spins $s$ is sufficiently large. We also prove the 
absence of long range order when $\alpha>3$ for any spin value.