  In this study, we investigate the energy landscape of the Ising and Potts
models on fixed and finite but large three-dimensional (3D) lattices where no
external field exists and quantitatively characterize the metastable behavior
of the associated Glauber dynamics in the very low temperature regime. Such
analyses for the models with non-zero external magnetic fields have been
extensively performed over the past two decades; however, models without
external fields remained uninvestigated. Recently, the corresponding
investigation has been conducted for the two-dimensional (2D) model without an
external field, and in this study, we further extend these successes to the 3D
model, which has a far more complicated energy landscape than the 2D one. In
particular, we provide a detailed description of the highly complex plateau
structure of saddle configurations between ground states and then analyze the
typical behavior of the Glauber dynamics thereon. Thus, we acheive a
quantitatively precise analysis of metastability, including the Eyring-Kramers
law, the Markov chain model reduction, and a full characterization of
metastable transition paths.
