  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, Journal of Statistical
Physics, 150: 1080-1114, 2013] and [Landim and Lemire, Journal of Statistical
Physics, 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.
