# Topology Controlled Potts Coarsening

## TL;DR

This paper studies the long-time relaxation and final states of the q-state kinetic Potts model on a triangular lattice, revealing unusual topological features and scaling behaviors in the coarsening process.

## Contribution

It uncovers novel topological features and anomalous scaling laws in the Potts model's coarsening dynamics on a triangular lattice, especially for q=3.

## Key findings

- Final states include ground, frozen three-hexagon, and stripe states.
- Relaxation time to frozen states scales as L^2 log L.
- New topological features and behaviors for q=3 and q>3.

## Abstract

We uncover unusual topological features in the long-time relaxation of the $q$-state kinetic Potts ferromagnet on the triangular lattice that is instantaneously quenched to zero temperature from a zero-magnetization initial state. For $q=3$, the final state is either: the ground state (frequency $\approx 0.75$), a frozen three-hexagon state (frequency $\approx 0.16$), a two-stripe state (frequency $\approx 0.09$), or a three-stripe state (frequency $<2\times 10^{-4}$). Other final state topologies, such as states with more than 3 hexagons, occur with probability $10^{-5}$ or smaller, for $q=3$. The relaxation to the frozen three-hexagon state is governed by a time that scales as $L^2\ln L$. We provide a heuristic argument for this anomalous scaling and present additional new features of Potts coarsening on the triangular lattice for $q=3$ and for $q>3$.