High-degeneracy Potts coarsening

TL;DR

This study investigates the zero-temperature dynamics of a high-degeneracy Potts ferromagnet on triangular lattices, revealing dominant ground states and rare complex configurations through extensive simulations.

Contribution

It provides new insights into the final state probabilities and the emergence of complex configurations in high-degeneracy Potts models under zero-temperature quench.

Findings

Ground state reached with probability ~0.71

Three-hexagon states occur with probability ~0.26

Spanning stripe states appear with probability ~0.03

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.