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By controlling the vortex core energy, the three-state ferromagnetic Pottsmodel can exhibit two types of topological paradigms, including thequasi-long-range ordered phase and the vortex lattice phase [PRL 116, 097206(2016)]. Here, by Monte Carlo simulations using an effective worm algorithm, weshow that by controlling the vortex core energy, the antiferromagnetic Pottsmodel can also exhibit the two topological phases, more interestingly, the twotopological phases can overlap with each other.

Overlap of two topological phases in the antiferromagnetic Potts model