Local Ward identities and the decay of correlations in ferromagnetics

Using local Ward identities we prove a number of correlation inequalities for N-component, isotropically coupled, pair interacting ferromagnets; some for all N >= 2 and some for N = 2,3,4. These are used to prove a mass gap above the mean field temperature, for all N >= 2. For N = 2,3,4 we prove an upper bound on a critical exponent, and a lower bound on the susceptability which diverges as m → 0. (orig.)