Metastability and nucleation for the Blume-Capel model. Different mechanisms of transition

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 Bred magnetic field it, and chemical potential lambda 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 line ii = 2 lambda is crossed.