Ising models on locally tree-like graphs
By Amir Dembo, Andrea Montanari. 2008
208 citations recorded by the source corpus.
We consider Ising models on graphs that converge locally to trees. Examples include random regular graphs with bounded degree and uniformly random graphs with bounded average degree. We prove that the `cavity' prediction for the limiting free energy per spin is correct for any temperature and external field. Further, local marginals can be approximated by iterating a set of mean field (cavity) equations. Both results are achieved by proving the local convergence of the Boltzmann distribution on the original graph to the Boltzmann distribution on the appropriate infinite random tree.
Subfields: Condensed Matter Physics, Mathematical Physics, Statistics and Probability
View Paper: https://www.semanticscholar.org/paper/a58f47045f1d84430d23799565c65c60cf40f951
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In Condensed Matter Physics
In Mathematical Physics
In Statistics and Probability
Citations in the corpus
- Random Graphs and Complex Networks (2016, background): “For example, Dembo and Montanari (2010) crucially rely on it in order to identify the limiting pressure for the Ising model on the configuration model.”
- Statistical physics of inference: thresholds and algorithms (2015, unknown): “[61] Amir Dembo, Andrea Montanari, et al.”