Antiferromagnetic Potts model on the Erdos-Renyi random graph

Details Antiferromagnetic Potts model on the Erdos-Renyi random graph Antiferromagnetic Potts model on the Erdos-Renyi random graph

2011-06-23

arxiv.org/abs/1106.4714v3

Mathematics

Probability

39 pages, 2 figures, references added, Outlook/Summary added

Scientific paper

We study the antiferromagnetic Potts model on the Erdos-Renyi random graph. By identifying a suitable interpolation structure and proving an extended variational principle we show that the replica symmetric solution is an upper bound for the limiting pressure which can be recovered in the framework of Derrida-Ruelle probability cascades. A comparison theorem with a mixed model made of a mean field Potts-antiferromagnet plus a Potts-Sherrington-Kirkpatrick model allows to show that the replica symmetric solution is exact at high temperatures.

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