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Counting in two-spin models on d-regular graphs

Sly, Allan; Sun, Nike


We establish that the normalized log-partition function of any two-spin system on bipartite locally tree-like graphs converges to a limiting “free energy density” which coincides with the (nonrigorous) Bethe prediction of statistical physics. Using this result, we characterize the local structure of two-spin systems on locally tree-like bipartite expander graphs without the use of the second moment method employed in previous works on these questions. As a consequence, we show that for...[Show more]

CollectionsANU Research Publications
Date published: 2014
Type: Journal article
Source: The Annals of Probability
DOI: 10.1214/13-AOP888
Access Rights: Open Access


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