The Ising fusion category lattice model features a symmetric critical phase equivalent to the Ising model, a categorical ferromagnetic phase with threefold degeneracy, and a critical categorical antiferromagnetic phase with fourfold degeneracy described by an Ising CFT.
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A method is given to construct UV anyonic chain lattice models from SymTFT data realizing IR phases and transitions with non-invertible symmetries, illustrated with Rep(S3).
Constructs Z_N extended fusion rings and modular partition functions for nonanomalous subgroups, extending to multicomponent systems and orbifoldings in CFTs.