Metastability of Blume–Capel Model with Zero Chemical Potential and Zero External Field

Kim, Seonwoo

doi:10.1007/s10955-021-02823-0

Cited by 8 publications

(2 citation statements)

References 22 publications

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“…The metastable behavior of this model was investigated in [16,18,19,26,27,41] under a non-zero external field. In our companion paper [24], we analyze the metastable behavior of the Blume-Capel model under a zero external field and zero chemical potential. We refer to [19,26,41] for detailed history and perspectives of the metastability in this model.…”

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Energy Landscape and Metastability of Stochastic Ising and Potts Models on Three-dimensional Lattices Without External Fields

Kim¹,

Seo²

2021

Preprint

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In this article, we investigate the metastable behaviors of the Glauber dynamics associated with Ising and Potts models on fixed, finite, but large lattices of dimensions two or three in the very-low-temperature regime. Metastability analyses of these models for non-zero external magnetic fields have been extensively researched during the last two decades; however, models without external fields remained uninvestigated. Recently, [Nardi and Zocca, Stochastic Processes and thier Applications, 129: 4556-4575, 2019] analyzed for the first time the two-dimensional case and obtained several large-deviationtype results for the metastability, by implementing the so-called pathwise approach. In the current article, we comprehensively extend these results in two ways. First, we obtain more refined results, including the Eyring-Kramers law, Markov-chain-model reductions, and a full characterization of metastable transition paths for the two-dimensional model. Second, we perform the corresponding analyses for the three-dimensional case. To this end, we derive precise descriptions of the energy landscape, which is particularly complex in the three-dimensional case, and then analyze the typical behavior of the Glauber dynamics on a suitable neighborhood of a very large set of complicated saddle configurations.

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“…This concludes our discussion on open boundary conditions. We refer to our companion paper [24] for a more detailed exposition of the discussion on open boundary conditions.…”

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confidence: 99%

Energy Landscape and Metastability of Stochastic Ising and Potts Models on Three-dimensional Lattices Without External Fields

Kim¹,

Seo²

2021

Preprint

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Metastability of Ising and Potts Models Without External Fields in Large Volumes at Low Temperatures

Kim

Seo

2022

Commun. Math. Phys.

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Periodic Gibbs Measures and Their Extremality for the HC-Blume–Capel Model in the Case of a Wand with a Chemical Potential on a Cayley Tree

Khatamov

2024

Math Notes

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Metastability of Blume–Capel Model with Zero Chemical Potential and Zero External Field

Cited by 8 publications

References 22 publications

Energy Landscape and Metastability of Stochastic Ising and Potts Models on Three-dimensional Lattices Without External Fields

Energy Landscape and Metastability of Stochastic Ising and Potts Models on Three-dimensional Lattices Without External Fields

Metastability of Ising and Potts Models Without External Fields in Large Volumes at Low Temperatures

Periodic Gibbs Measures and Their Extremality for the HC-Blume–Capel Model in the Case of a Wand with a Chemical Potential on a Cayley Tree

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