For the antiferromagnetic Potts model on the Erdos-Renyi graph, Bayati, Gamarnik and Tetali showed how to extend Guerra and Toninelli's, and Franz and Leone's interpolation to the binomial version of the model. Panchenko's version of the variational principle applies, too, which is stronger than the A-S-S scheme. There has been much physics work, by Krzakala and Zdeborova, most of it rigorous in light of interpolation and Guerra's RSB type bounds. With Dommers, Contucci and Giardina, we considered a subset of the high T region, with 0 external field, and proved triviality, following Guerra and Toninelli's first paper. I'll talk about that.
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