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.

在这项研究中，我们研究了与具有零化学势和零外场的 Blume-Capel 模型相关的 Metropolis 型芒硝动力学在极低温度下的亚稳态行为。在 Cirillo 和 Nardi (J Stat Phys 150:1080–1114, 2013) 和 Landim and Lemire (J Stat Phys 164:346–376, 2016) 中对具有零化学势和正小外场的相同模型进行了相应的分析. 我们在我们的设置中获得了亚稳态行为的大偏差类型和潜在理论结果。为此，我们对能量景观进行了高度彻底的调查，发现不存在关键配置，或者存在一个巨大的马鞍配置平台。