Antiferromagnetic Potts model on the Erdos-Renyi random graph

Abstract

We study the antiferromagnetic Potts model on the Poissonian Erdös-Rényi random graph. By identifying a suitable interpolation structure and an extended variational principle, together with a positive temperature second-moment analysis we prove the existence of a phase transition at a positive critical temperature. Upper and lower bounds on the temperature critical value are obtained from the stability analysis of the replica symmetric solution (recovered in the framework of Derrida-Ruelle probability cascades)and from a positive entropy argument.

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References in corpus (7)

• Broken Replica Symmetry Bounds in the Mean Field Spin Glass Model
• Phase Transitions in the Coloring of Random Graphs
• Ising models on locally tree-like graphs
• Characterization of invariant measures at the leading edge for competing particle systems
• The high temperature region of the Viana-Bray diluted spin glass model
• Ising models on power-law random graphs
• Potts Glass on Random Graphs

Cited by in corpus (5)

• Information-theoretic thresholds from the cavity method
• The condensation phase transition in random graph coloring
• Charting the replica symmetric phase
• A positive temperature phase transition in random hypergraph 2-coloring
• Spin systems on Bethe lattices