Large deviations for the annealed Ising model on inhomogeneous random graphs: spins and degrees

TL;DR

This paper establishes a large deviations principle for the total spin and edges in the annealed Ising model on inhomogeneous random graphs, revealing how annealing influences vertex degrees and induces correlations.

Contribution

It introduces a large deviations framework for the annealed Ising model on generalized random graphs, with detailed analysis of degree modifications and correlation structures.

Findings

Large deviations principle for total spin and edges.

Annealing alters vertex degree distributions.

Induces correlations in the random graph structure.

Abstract

We prove a large deviations principle for the total spin and the number of edges under the annealed Ising measure on generalized random graphs. We also give detailed results on how the annealing over the Ising model changes the degrees of the vertices in the graph and show how it gives rise to interesting correlated random graphs.