Topology-controlled potts coarsening

Denholm, J. and Redner, S. (2019) Topology-controlled potts coarsening. Physical Review E, 99 (6). 062142. ISSN 2470-0053 (https://doi.org/10.1103/PhysRevE.99.062142)

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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.

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