Counting in two-spin models on d-regular graphs
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]
|Collections||ANU Research Publications|
|Source:||The Annals of Probability|
|01_Sly_Counting_in_two-spin_models_on_2014.pdf||Published Version||385.77 kB||Adobe PDF|
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