  In this article, we investigate the metastable behaviors of the Glauber
dynamics associated with Ising and Potts models on fixed, finite, but large
lattices of dimensions two or three in the very-low-temperature regime.
Metastability analyses of these models for non-zero external magnetic fields
have been extensively researched during the last two decades; however, models
without external fields remained uninvestigated. Recently, [Nardi and Zocca,
Stochastic Processes and thier Applications, 129: 4556-4575, 2019] analyzed for
the first time the two-dimensional case and obtained several
large-deviation-type results for the metastability, by implementing the
so-called pathwise approach. In the current article, we comprehensively extend
these results in two ways. First, we obtain more refined results, including the
Eyring-Kramers law, Markov-chain-model reductions, and a full characterization
of metastable transition paths for the two-dimensional model. Second, we
perform the corresponding analyses for the three-dimensional case. To this end,
we derive precise descriptions of the energy landscape, which is particularly
complex in the three-dimensional case, and then analyze the typical behavior of
the Glauber dynamics on a suitable neighborhood of a very large set of
complicated saddle configurations.
