# Critical behavior of the annealed ising model on random regular graphs

## TL;DR

This paper investigates the critical phenomena of the annealed Ising model on random regular graphs, identifying critical exponents and establishing a novel limit theorem for magnetization scaling.

## Contribution

It extends previous work by analyzing the critical behavior and deriving a non-standard limit theorem for the magnetization in the annealed Ising model on all random regular graphs.

## Key findings

- Determined the critical exponents for the model.
- Proved a limit theorem with magnetization scaled by n^{3/4}.
- Identified the limiting distribution of the scaled magnetization.

## Abstract

In [17], the authors have defined an annealed Ising model on random graphs and proved limit theorems for the magnetization of this model on some random graphs including random 2-regular graphs. Then in [11], we generalized their results to the class of all random regular graphs. In this paper, we study the critical behavior of this model. In particular, we determine the critical exponents and prove a non standard limit theorem that the magnetization scaled by n 3/4 converges to a specific random variable, with n the number of vertices of random regular graphs.