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In this study, we investigate the energy landscape of the Ising and Pottsmodels on fixed and finite but large three-dimensional (3D) lattices where noexternal field exists and quantitatively characterize the metastable behaviorof the associated Glauber dynamics in the very low temperature regime. Suchanalyses for the models with non-zero external magnetic fields have beenextensively performed over the past two decades; however, models withoutexternal fields remained uninvestigated. Recently, the correspondinginvestigation has been conducted for the two-dimensional (2D) model without anexternal field, and in this study, we further extend these successes to the 3Dmodel, which has a far more complicated energy landscape than the 2D one. Inparticular, we provide a detailed description of the highly complex plateaustructure of saddle configurations between ground states and then analyze thetypical behavior of the Glauber dynamics thereon. Thus, we acheive aquantitatively precise analysis of metastability, including the Eyring-Kramerslaw, the Markov chain model reduction, and a full characterization ofmetastable transition paths.

Energy Landscape and Metastability of Stochastic Ising and Potts Models on Three-dimensional Lattices Without External Fields