METASTABILITY AND NUCLEATION FOR THE BLUME-CAPEL MODEL - DIFFERENT MECHANISMS OF TRANSITION

We study metastability and nucleation for the Blume-Capel model: a Fer romagnetic nearest neighbor two-dimensional lattice system with spin v ariables taking values in {-1, 0, +1}. We consider large but finite vo lume, small Bred magnetic field it, and chemical potential lambda in t he 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 typic al tube of trajectories during the transition. We show that, unexpecte dly, the mechanism of transition changes abruptly when the line ii = 2 lambda is crossed.