Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Annealed central limit theorems for the Ising model on random graphs   The aim of this paper is to prove central limit theorems with respect to the
annealed measure for the magnetization rescaled by $\sqrt{N}$ of Ising models
on random graphs. More precisely, we consider the general rank-1 inhomogeneous
random graph (or generalized random graph), the 2-regular configuration model
and the configuration model with degrees 1 and 2. For the generalized random
graph, we first show the existence of a finite annealed inverse critical
temperature $0 \leq \beta^{\mathrm \scriptscriptstyle an}_c < \infty$ and then
prove our results in the uniqueness regime, i.e., the values of inverse
temperature $\beta$ and external magnetic field $B$ for which either $\beta <
\beta^{\mathrm \scriptscriptstyle an}_c$ and $B=0$, or $\beta>0$ and $B \neq
0$. In the case of the configuration model, the central limit theorem holds in
the whole region of the parameters $\beta$ and $B$, because phase transitions
do not exist for these systems as they are closely related to one-dimensional
Ising models. Our proofs are based on explicit computations that are possible
since the Ising model on the generalized random graph in the annealed setting
is reduced to an inhomogeneous Curie-Weiss model, while the analysis of the
configuration model with degrees only taking values 1 and 2 relies on that of
the classical one-dimensional Ising model.

5
The categories of this paper are: gr-qc
1
The categories of this paper are: cs
17
The categories of this paper are: q-fin
8
The categories of this paper are: hep-ex
34
The categories of this paper are: chem-ph
31
The categories of this paper are: ao-sci
26
The categories of this paper are: bayes-an
3
The categories of this paper are: physics
23
The categories of this paper are: solv-int
18
The categories of this paper are: econ
12
The categories of this paper are: nucl-th
24
The categories of this paper are: dg-ga
35
The categories of this paper are: mtrl-th
7
The categories of this paper are: hep-th
13
The categories of this paper are: quant-ph
20
The categories of this paper are: acc-phys