Topology-controlled potts coarsening

J. Denholm, S. Redner

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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 L2 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.
Original languageEnglish
Article number062142
Number of pages7
JournalPhysical Review E
Volume99
Issue number6
DOIs
Publication statusPublished - 28 Jun 2019

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Keywords

  • Potts ferromagnet
  • topological characterization
  • Potts coarsening

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