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Antiferromagnetic Potts Model on the Erdős-Rényi Random Graph

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Abstract

We study the antiferromagnetic Potts model on the Poissonian Erdős-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 an entropy positivity argument.

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Authors and Affiliations

  1. Università di Bologna, Piazza di Porta S.Donato 5, 40127, Bologna, Italy

    Pierluigi Contucci

  2. Eindhoven University of Technology, Department of Mathematics and Computer Science, P.O. Box 513, 5600 MB, Eindhoven, The Netherlands

    Sander Dommers

  3. Università di Modena e Reggio Emilia, viale A. Allegri, 9, 42121, Reggio Emilia, Italy

    Cristian Giardinà

  4. University of Rochester, Department of Mathematics, Rochester, NY, 14627, USA

    Shannon Starr

Authors
  1. Pierluigi Contucci
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  2. Sander Dommers
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  3. Cristian Giardinà
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  4. Shannon Starr
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Corresponding author

Correspondence to Pierluigi Contucci.

Additional information

Communicated by M. Aizenman

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Contucci, P., Dommers, S., Giardinà, C. et al. Antiferromagnetic Potts Model on the Erdős-Rényi Random Graph. Commun. Math. Phys. 323, 517–554 (2013). https://doi.org/10.1007/s00220-013-1778-y

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  • DOI: https://doi.org/10.1007/s00220-013-1778-y

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