The GHS and other correlation inequalities for a class of even ferromagnets

We prove the GHS inequality for families of random variables which arise in certain ferromagnetic models of statistical mechanics and quantum field theory. These include spin -1/2 Ising models, φ{symbol}⁴ field theories, and other continuous spin models. The proofs are based on the properties of a class G^- of probability measures which contains all measures of the form const exp(-V(x))dx, where V is even and continuously differentiable and dV/dx is convex on [0, ∞). A new proof of the GKS inequalities using similar ideas is also given.