High-degeneracy Potts coarsening

Denholm, J. (2021) High-degeneracy Potts coarsening. Physical Review E, 103 (1). 012119. ISSN 1539-3755

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    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 ≤ L ≤ 128 and set the number of spin states q equal to the number of lattice sites L×L. The ground state is the most abundant final state, and is reached with probability ≈ 0.71. Three-hexagon states occur with probability ≈ 0.26, and hexagonal tessellations with more than three clusters form with probabilities of O(10−3 ) or less. Spanning stripe states—where the domain walls run along one of the three lattice directions—appear with probability ≈ 0.03. “Blinker” configurations, which contain perpetually flippable spins, also emerge, but with a probability that is vanishingly small with the system size.