Asymptotics of decay of correlations for lattice spin fields at high temperatures. I. The Ising model

W find the asymptotic decrease of correlations <σA+y, σB>, y ε Zv+1, |y|→∞, in the Ising model at high temperatures. For the case when monomials σA and σB both are odd, using the saddle-point method, we find the asymptotics of the correlations for any dimension v. For even monomials σA, σB we formulate a general hypothesis about the form of the asymptotics and confirm it in two cases: (1) v=1 and the vector y has an arbitrary direction, (2) y is directed along a fixed axis and arbitrary v. Here we use besides the saddle-point method, some arguments from scattering theory