Upper bounds on the transition temperature of classical n.n. ferromagnetic systems for general n and d

A differential equation is obtained for the spin-spin correlation function of a system of n-component classical spins interacting via a nearest neighbour ferromagnetic interaction. The differential equation makes it possible to obtain upper bounds on the correlation length and the transition temperature. It also makes it possible to relate the correlation length with the energy per spin and to obtain a necessary condition for the existence of the phase transition in terms of the energy per spin.