Decay of correlations in multicomponent ferromagnets with long-range interaction (Q817444)

The estimate \(g_N(l)\leq Ng_1(l)\) for the two-point correlation functions of \(N\)-component ferromagnetic spin models on the lattice \(\mathbb Z^d\) with arbitrary \(d\) has been proven. By this estimate the decay of \(g_N(l)\) as \(|l|\to+\infty\) is shown to be the same as the decay of the pair-interaction potential \(J(l)\leq J_0(|l|+1)^{-d\gamma}\), \(\gamma>1\) if the temperature is above the transition point \(T_C (1)\) of the corresponding one-component model. For `large enough' temperatures, the decay of \(g_N(l)\) has been obtained for all types of the decay of \(J(l)\).