Weakening of correlations in one-dimensional spin systems with long-range interaction

It is shown that in a one-dimensional ferromagnet with long-range potential that decreases as $r^{-\alpha}$, $1<\alpha$, the binary correlation function decreases asymptotically at high temperatures in the same manner as the interaction potential. A theorem of Griffiths, which gives bounds for the higher correlation functions, is also generalized.