Cluster expansion methods in rigorous statistical mechanics

TL;DR

This paper introduces cluster expansion methods within rigorous statistical mechanics, serving as preliminary class notes for graduate students, covering foundational concepts and techniques in the field.

Contribution

It provides an initial, comprehensive overview of cluster expansion methods tailored for educational purposes in rigorous statistical mechanics.

Findings

Introduces foundational cluster expansion techniques

Serves as educational material for graduate courses

Highlights areas needing further development

Abstract

This draft is intended to be used as class notes for a grad course on rigorous statistical mechanics at math department of UFMG. It should be considered as a very prelimivary version and a work in progress. Several chapters lack references, exercises, and revision.