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Solutions of the variational problem in the Curie--Weiss--Potts model

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  • Wang, Kongming

Abstract

The variational problem for the Curie--Weiss--Potts model is solved completely. The results extend those of Ellis and Wang (1990, 1992), in which we study limit theorems and parameter estimations for the model and consider only the case of zero external field. In contrast to the Curie--Weiss model, this model has phase transitions in non-zero external field. All the solutions of the variational problem are non-degenerate points, so all the results in Ellis and Wang (1990, 1992) can be easily extended to the case considered here. We will also point out that simultaneous parameter estimation is impossible.

Suggested Citation

  • Wang, Kongming, 1994. "Solutions of the variational problem in the Curie--Weiss--Potts model," Stochastic Processes and their Applications, Elsevier, vol. 50(2), pages 245-252, April.
    • Handle: RePEc:eee:spapps:v:50:y:1994:i:2:p:245-252
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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. Cerioli, Andrea, 2002. "Tests of homogeneity for spatial populations," Statistics & Probability Letters, Elsevier, vol. 58(2), pages 123-130, June.
    4. 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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