Comparison of Ising models under change of a priori measure

Abstract

We study comparison of correlation functions for ferromagnetic generalized Ising models with two different a priori measures. One purpose of this note is to publicize some unpublished 45 year old work of Daniel Wells on the issue. We then prove results for the a priori measures associated to one component of $D$-vectors uniformly distributed on the unit sphere and also the case of spin $S$ ($2S+1$ equally spaced values symmetric about $0$ and with equal weights) that improves some 50 year old bounds of Griffiths on transition temperatures.