Local Ward identities and the decay of correlations in ferromagnets

Abstract

Using local Ward identities we prove a number of correlation inequalities forN-component, isotropically coupled, pair interacting ferromagnets; some for allN≧2 and some forN=2, 3, 4. These are used to prove a mass gap above the mean field temperature, for allN≧2. ForN=2, 3, 4 we prove an upper bound on a critical exponent, and a lower bound on the susceptability which diverges asm→0.