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.

• Received 29 September 2020
• Accepted 27 December 2020

DOI:https://doi.org/10.1103/PhysRevE.103.012119