Comparison of Ising Models Under Change of Apriori Measure

TL;DR

This paper compares correlation functions in ferromagnetic Ising models with different initial measures, revisiting historical work and providing new bounds on transition temperatures for specific measure types.

Contribution

It revisits and publicizes 45-year-old unpublished work and introduces new results for measures on D-vectors and spin systems, improving bounds on transition temperatures.

Findings

Revisits historical results on Ising model correlations.

Provides new bounds for transition temperatures with specific measures.

Enhances understanding of measure effects on ferromagnetic models.

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 One purpose of this note is to publicize some unpublished 45 year old work of Daniel Wells on the issue.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.