论文标题
具有一般相互作用的三态POTTS模型的亚竞争力
Metastability of the three-state Potts model with general interactions
论文作者
论文摘要
我们在二维周期性矩形晶格上考虑了POTTS模型，并带有一般耦合常数$ J_ {ij}> 0 $，其中$ i，j \ in \ in \ {1,2,3 \} $是可能的旋转值（或颜色）。因此，所得能量格局比原始ISING或POTTS模型要复杂得多。该系统根据Glauber型旋转式动力学发展。我们专注于参数空间的区域，其中有两个对称亚稳态状态和一个稳定状态，并且亚稳态状态之间的直接路径高度等于任何亚稳态状态和稳定状态之间的直接路径的高度。我们研究了概率和预期的亚稳态过渡时间，当反向温度$β$倾向于无穷大时，动力学的混合时间和系统的光谱间隙。然后，我们确定在亚稳态过渡期间访问的所有关键配置。
We consider the Potts model on a two-dimensional periodic rectangular lattice with general coupling constants $J_{ij}>0$, where $i,j\in\{1,2,3\}$ are the possible spin values (or colors). The resulting energy landscape is thus significantly more complex than in the original Ising or Potts models. The system evolves according to a Glauber-type spin-flipping dynamics. We focus on a region of the parameter space where there are two symmetric metastable states and a stable state, and the height of a direct path between the metastable states is equal to the height of a direct path between any metastable state and the stable state. We study the metastable transition time in probability and in expectation, the mixing time of the dynamics and the spectral gap of the system when the inverse temperature $β$ tends to infinity. Then, we identify all the critical configurations that are visited with high probability during the metastable transition.
