Comparison of Ising Models Under Change of Apriori Measure

Abstract

We study comparison of correlation functions for ferromagnetic generalized Ising models with two different apriori 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 One purpose of this note is to publicize some unpublished 45 year old work of Daniel Wells on the issue.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 apriori 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.