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

In this study, we investigate the metastable behavior of Metropolis-type Glauber dynamics associated with the Blume–Capel model with zero chemical potential and zero external field at very low temperatures. The corresponding analyses for the same model with zero chemical potential and positive small external field were performed in Cirillo and Nardi (J Stat Phys 150:1080–1114, 2013) and Landim and Lemire (J Stat Phys 164:346–376, 2016). We obtain both large deviation-type and potential-theoretic results on the metastable behavior in our setting. To this end, we perform highly thorough investigation on the energy landscape, where it is revealed that no critical configurations exist and alternatively a massive flat plateau of saddle configurations resides therein.