High-degeneracy Potts coarsening

Abstract

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 $\mathcal{O}(10^{-3})$ 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.