High-degeneracy Potts coarsening

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.