Some positive definite functions on sets and their application to the Ising model

Abstract

Consideration of correlation inequalities for Ising ferromagnets with arbitrary spins has led to the discovery of a class of positive definite functions on sets. These functions are linear combinations of the functions which enter into Muirhead's Theorem. We prove these functions to be positive definite and also show how they can be applied to the Ising problem to prove Griffiths second inequality for arbitrary spins.