Topology-controlled Potts coarsening.

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 ≈0.75), a frozen three-hexagon state (frequency ≈0.16), a two-stripe state (frequency ≈0.09), or a three-stripe state (frequency <2×10^{-4}). Other final state topologies, such as states with more than three 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}lnL. 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.