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Metastability of the Two-Dimensional Blume–Capel Model with Zero Chemical Potential and Small Magnetic Field

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Abstract

We consider the two-dimensional Blume–Capel model with zero chemical potential and small magnetic field evolving on a large but finite torus. We obtain sharp estimates for the transition time, we characterize the set of critical configurations, and we prove the metastable behavior of the dynamics as the temperature vanishes.

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Acknowledgments

The authors wish to thank O. Benois and M. Mourragui for fruitful discussions, and one of the referees for her/his careful reading which permitted to improve the presentation of the article.

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Authors and Affiliations

  1. IMPA, Estrada Dona Castorina 110, CEP 22460-320, Rio de Janeiro, Brazil

    C. Landim

  2. CNRS UMR 6085, Université de Rouen, Avenue de l’Université, Technopôle du Madrillet, BP. 12, 76801, Saint-Étienne-du-Rouvray, France

    C. Landim & P. Lemire

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  1. C. Landim
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  2. P. Lemire
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Landim, C., Lemire, P. Metastability of the Two-Dimensional Blume–Capel Model with Zero Chemical Potential and Small Magnetic Field. J Stat Phys 164, 346–376 (2016). https://doi.org/10.1007/s10955-016-1550-8

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  • DOI: https://doi.org/10.1007/s10955-016-1550-8

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