I examine the fate of a kinetic Potts ferromagnet with a high ground-state degeneracy that undergoes a deep quench to zero temperature. I consider single spin-flip dynamics on triangular lattices of linear dimension $8\le L\le 128$ and set the number of spin states $q$ equal to the number of lattice sites $L\times L$. The ground state is the most abundant final state, and is reached with probability $\approx 0.71$. Three-hexagon states occur with probability $\approx 0.26$, and hexagonal tessellations with more than three clusters form with probabilities of $O\left({10}^{-3}\right)$ or less. Spanning stripe states—where the domain walls run along one of the three lattice directions—appear with probability $\approx 0.03$. “Blinker” configurations, which contain perpetually flippable spins, also emerge, but with a probability that is vanishingly small with the system size.

中文翻译：

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高退化Potts粗化

我研究了具有高基态简并性并经历深淬火至零温度的动力学Potts铁磁体的命运。我考虑线性尺寸的三角形晶格上的单自旋翻转动力学$8\le \mathrm{大号}\le 128$ 并设置旋转状态数 $q$ 等于点阵数 $\mathrm{大号}\times \mathrm{大号}$。基态是最丰富的最终状态，并且有可能达到$\approx 0.71$。三六角态发生的可能性$\approx 0.26$以及具有三个以上簇的六边形方格形成，概率为 $Ø（{10}^{-3}）$或更少。跨条带状态（其中畴壁沿三个晶格方向之一延伸）以概率出现$\approx 0.03$。也出现了包含永久可翻转自旋的“闪烁器”配置，但是这种可能性随着系统规模的减小而逐渐消失。