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Limit theorems and coexistence probabilities for the Curie-Weiss Potts model with an external field

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  • Gandolfo, Daniel
  • Ruiz, Jean
  • Wouts, Marc

Abstract

The Curie-Weiss Potts model is a mean field version of the well-known Potts model. In this model, the critical line [beta]=[beta]c(h) is explicitly known and corresponds to a first-order transition when q>2. In the present paper we describe the fluctuations of the density vector in the whole domain [beta][greater-or-equal, slanted]0 and h[greater-or-equal, slanted]0, including the conditional fluctuations on the critical line and the non-Gaussian fluctuations at the extremity of the critical line. The probabilities of each of the two thermodynamically stable states on the critical line are also computed. Similar results are inferred for the random-cluster model on the complete graph.

Suggested Citation

  • Gandolfo, Daniel & Ruiz, Jean & Wouts, Marc, 2010. "Limit theorems and coexistence probabilities for the Curie-Weiss Potts model with an external field," Stochastic Processes and their Applications, Elsevier, vol. 120(1), pages 84-104, January.
    • Handle: RePEc:eee:spapps:v:120:y:2010:i:1:p:84-104
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    References listed on IDEAS

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    1. Ellis, Richard S. & Wang, Kongming, 1990. "Limit theorems for the empirical vector of the Curie-Weiss-Potts model," Stochastic Processes and their Applications, Elsevier, vol. 35(1), pages 59-79, June.
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    Cited by:

    1. Nardi, Francesca R. & Zocca, Alessandro, 2019. "Tunneling behavior of Ising and Potts models in the low-temperature regime," Stochastic Processes and their Applications, Elsevier, vol. 129(11), pages 4556-4575.
    2. Martschink, Bastian, 2014. "Bounds on convergence for the empirical vector of the Curie–Weiss–Potts model with a non-zero external field vector," Statistics & Probability Letters, Elsevier, vol. 88(C), pages 118-126.
    3. Bet, Gianmarco & Gallo, Anna & Nardi, F.R., 2024. "Metastability for the degenerate Potts Model with positive external magnetic field under Glauber dynamics," Stochastic Processes and their Applications, Elsevier, vol. 172(C).

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