We consider the ferromagnetic q-state Potts model with zero external field in a finite volume evolving according to Glauber-type dynamics described by the Metropolis algorithm in the low temperature asymptotic limit. Our analysis concerns the multi-spin system that has q stable equilibria. Focusing on grid graphs with periodic boundary conditions, we study the tunneling between two stable states and from one stable state to the set of all other stable states. In both cases we identify the set of gates for the transition and prove that this set has to be crossed with high probability during the transition. Moreover, we identify the tube of typical paths and prove that the probability to deviate from it during the transition is exponentially small.

我们考虑在有限体积中具有零外场的铁磁q 态Potts 模型，该模型根据在低温渐近极限下由 Metropolis 算法描述的 Glauber 型动力学演化。我们的分析涉及具有q 个稳定平衡的多自旋系统。专注于具有周期性边界条件的网格图，我们研究了两个稳定状态之间以及从一个稳定状态到所有其他稳定状态的隧道。在这两种情况下，我们都确定了转换的门组，并证明在转换期间必须以高概率穿越该组。此外，我们确定了典型路径的管道，并证明在过渡期间偏离它的概率是指数级的。