Infinite Volume Limit for Correlation functions in the Dipole Gas

TL;DR

This paper analyzes a classical lattice dipole gas in dimensions three and higher, demonstrating that correlation functions reach an infinite volume limit and providing decay estimates through renormalization group analysis.

Contribution

It establishes the existence of infinite volume limits for correlation functions in the dipole gas and offers decay estimates using renormalization group techniques.

Findings

Correlation functions have an infinite volume limit.

Decay estimates for correlation functions are obtained.

Results apply to low activity dipole gases in dimensions d ≥ 3.

Abstract

We study a classical lattice dipole gas with low activity in dimension $d \geq 3$. We investigate long distance properties by a renormalization group analysis. We prove that various correlation functions have an infinite volume limit. We also get estimates on the decay of correlation functions.