# 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.

## Key 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.

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Source: https://tomesphere.com/paper/1701.08639