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Metastability of the three-state Potts model with general interactions

Gianmarco BetAnna GalloSeonwoo Kim
Aug 2022
摘要
We consider the Potts model on a two-dimensional periodic rectangular latticewith general coupling constants $J_{ij}>0$, where $i,j\in\{1,2,3\}$ are thepossible spin values (or colors). The resulting energy landscape is thussignificantly more complex than in the original Ising or Potts models. Thesystem evolves according to a Glauber-type spin-flipping dynamics. We focus ona region of the parameter space where there are two symmetric metastable statesand a stable state, and the height of a direct path between the metastablestates is equal to the height of a direct path between any metastable state andthe stable state. We study the metastable transition time in probability and inexpectation, the mixing time of the dynamics and the spectral gap of the systemwhen the inverse temperature $\beta$ tends to infinity. Then, we identify allthe critical configurations that are visited with high probability during themetastable transition.
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