Phase-diagram characterization of 2-group Potts models

Characterize the phase diagrams of the split and central 2-group Potts models and their gauged 2Rep(G)-Potts counterparts, including the phases associated with generalized symmetry breaking and topological order.

Background

The paper constructs lattice Potts Hamiltonians for split and central finite 2-group symmetries, together with their gauged models possessing 2Rep(G) symmetry. Several exactly solvable limits are identified, including phases with spontaneous generalized symmetry breaking and topological order.

Despite these solvable limits, the authors state that the overall phase structure of the models has not been systematically determined. Resolving this problem would clarify which phases occur in the lattice realizations and how they relate to the generalized symmetry and topological-order structures discussed in the paper.

References

We identified several exactly-solvable limits of our ${2+1}$d models, but a systematic characterization of their phase diagrams remains open.

— Lattice 2-group symmetries: operators, defects, and gauging  (2609.10682 - Brito et al., 9 Sep 2026) in Section Outlook, item 1, paragraph beginning “Related generalized Ising and Potts models”