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Metastability of the three-state Potts model with asymmetrical external field

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  • Ahn, Jeonghyun

Abstract

In this paper, we explore the metastable behavior of the Glauber dynamics associated with the three-state Potts model with an asymmetrical external field at a low-temperature regime. The model exhibits three monochromatic configurations: a unique stable state and two metastable states with different stability levels. We investigate metastable transitions, which are transitions from each metastable state to the ground state, separately and verify that the two transitions exhibit different behaviors.

Suggested Citation

  • Ahn, Jeonghyun, 2024. "Metastability of the three-state Potts model with asymmetrical external field," Stochastic Processes and their Applications, Elsevier, vol. 176(C).
    • Handle: RePEc:eee:spapps:v:176:y:2024:i:c:s0304414924001297
    DOI: 10.1016/j.spa.2024.104423
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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.
    2. 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.
    3. 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.
    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).
    5. Ellis, Richard S. & Wang, Kongming, 1992. "Limit theorems for maximum likelihood estimators in the Curie-Weiss-Potts model," Stochastic Processes and their Applications, Elsevier, vol. 40(2), pages 251-288, March.
    6. Baldassarri, Simone & Nardi, Francesca R., 2022. "Critical Droplets and sharp asymptotics for Kawasaki dynamics with weakly anisotropic interactions," Stochastic Processes and their Applications, Elsevier, vol. 147(C), pages 107-144.
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