Decay of the Two-Point Function in One-Dimensional O(N) Spin Models with   Long Range Interactions
  Using Griffiths and Lieb-Simon type inequalities, it is shown that the two-point function of ferromagnetic spin models with N components in one dimension decays like the interaction provided that N=1,2,3,4 and T > T_c. 
Herbert Spohn, Wilhelm Zwerger