Abstract
We study the three-state antiferromagnetic Potts model on the simple-cubic lattice, paying attention to the surface critical behaviors. When the nearest-neighboring interactions of the surface is tuned, we obtain a phase diagram similar to the XY model, owing to the emergent O(2) symmetry of the bulk critical point. For the ordinary transition, we get , and ; for the special transition, we get , and ; in the extraordinary-log phase, the surface correlation function decays logarithmically with decaying exponent , however, the correlation still decays algebraically with critical exponent . If the ferromagnetic next-nearest-neighboring surface interactions are added, we find two transition points, the first one is a special point between the ordinary phase and the extraordinary-log phase, the second one is a transition between the extraordinary-log phase and the symmetry-breaking phase, with critical exponent . The scaling behaviors of the second transition is very interesting, the surface spin-correlation function , and the surface squared staggered magnetization at this point decays logarithmically with exponent ; however, the surface structure factor with the smallest wave vector and the correlation function satisfy power-law decaying, with critical exponents and , respectively.
1 More- Received 1 May 2022
- Revised 29 May 2022
- Accepted 1 June 2022
DOI:https://doi.org/10.1103/PhysRevB.105.224415
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