Sublattice extraordinary-log phase and special points of the antiferromagnetic Potts model

We study the surface criticality of a three-state antiferromagnetic Potts model on simple cubic lattice, whose bulk critical behavior belongs to universality class XY because emergent O(2) symmetry. find that next-nearest-neighboring interactions can drive extraordinary-log phase an ordinary phase, and transition between two phases well-known special model. Further enhancing interactions, reappears, but main behaviors are shown in sublattices; point sublattice different class.