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math.PR2012★ 2 cited
The replica symmetric solution for Potts models on d-regular graphs
Amir Dembo, Andrea Montanari, Allan Sly +1
We provide an explicit formula for the limiting free energy density (log-partition function divided by the number of vertices) for ferromagnetic Potts models on uniformly sparse gr…
math.PR2012★ 59 cited
The computational hardness of counting in two-spin models on d-regular graphs
Allan Sly, Nike Sun
The class of two-spin systems contains several important models, including random independent sets and the Ising model of statistical physics. We show that for both the hard-core (…