Annealed limit theorems for the ising model on random regular graphs

TL;DR

This paper provides a new proof of annealed limit theorems for the Ising model on all random regular graphs and establishes the existence of annealed pressure for configuration model graphs.

Contribution

It introduces a unified proof approach for annealed limit theorems on all random regular graphs and extends results to configuration model graphs.

Findings

Proved annealed law of large numbers and CLT for all random regular graphs.

Established existence of annealed pressure for configuration model graphs.

Unified proof method applicable to a broad class of random graphs.

Abstract

In a recent paper [15], Giardin{\`a}, Giberti, Hofstad, Prioriello have proved a law of large number and a central limit theorem with respect to the annealed measure for the magnetization of the Ising model on some random graphs including the random 2-regular graph. We present a new proof of their results, which applies to all random regular graphs. In addition, we prove the existence of annealed pressure in the case of configuration model random graphs.