Cluster expansions and correlation functions

TL;DR

This paper introduces a new cluster expansion method applicable to both continuous and discrete systems, providing convergence criteria, correlation function estimates, and applications to classical, quantum, and lattice models.

Contribution

It develops a unified cluster expansion framework with an extended convergence criterion, enhancing analysis of correlation functions across various particle systems.

Findings

Established a convergence criterion extending Kotecky-Preiss

Derived expressions and estimates for correlation functions

Applied the framework to classical, quantum, and lattice systems

Abstract

A cluster expansion is proposed, that applies to both continuous and discrete systems. The assumption for its convergence involves an extension of the neat Kotecky-Preiss criterion. Expressions and estimates for correlation functions are also presented. The results are applied to systems of interacting classical and quantum particles, and to a lattice polymer model.