Griffiths Inequalities for some O(n) Classical Spin Models with $n\ge 3$

TL;DR

This paper proves the first and second Griffiths inequalities for certain classical O(n)-invariant spin models, including Euclidean quantum field theories, under specific integral transform conditions, expanding theoretical understanding of these models.

Contribution

It introduces a proof of Griffiths inequalities for O(n) models with n≥3, under a new integral transform condition, which was not previously established.

Findings

Griffiths inequalities are valid for O(n) models with n≥3

The proof applies to models including Euclidean quantum field theories

Examples illustrating the conditions are discussed

Abstract

The first and second Griffiths inequalities are proved for some classical O($n$)-invariant spin models (including Euclidean quantum field theories) for any $n$. The proof assumes a certain condition on an integral transform of the measure. Some examples are discussed.