Abstract
We study metastability and nucleation for the Blume-Capel model: a ferromagnetic nearest neighbor two-dimensional lattice system with spin variables taking values in {−1,0, +1}. We consider large but finite volume, small fixed magnetic fieldh, and chemical potential λ in the limit of zero temperature; we analyze the first excursion from the metastable −1 configuration to the stable +1 configuration. We compute the asymptotic behavior of the transition time and describe the typical tube of trajectories during the transition. We show that, unexpectedly, the mechanism of transition changes abruptly when the lineh=2λ is crossed.
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Cirillo, E.N.M., Olivieri, E. Metastability and nucleation for the Blume-Capel model. Different mechanisms of transition. J Stat Phys 83, 473–554 (1996). https://doi.org/10.1007/BF02183739
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DOI: https://doi.org/10.1007/BF02183739