Decay of correlations in multicomponent ferromagnets with long-range interaction

The estimate gN(l)≤Ng1(l) for the two-point correlation functions of N-component ferromagnetic spin models on the lattice ℤd with arbitrary d has been proven. By tis estimate the decay of gN(l) as |l|+∞ is shown to be the same as the decay of the pair-interaction potential j(l)≤J0(|l|+1)−dγ, γ>1, if the temperature is above the transition point TC (1) of the corresponding one-component model. For ‘large enough’ temperatures, the decay of gN(l) has been obtained for all types of the decay of J(l).