Generality of first-order transitions in subsystem-symmetric Ising models

Determine whether subsystem-symmetry breaking in a fully interacting, short-range three-dimensional Ising model can occur through a continuous phase transition and whether long-range subsystem ordering can be associated with genuine critical behavior.

Background

The thesis studies the Tetrahedral Ising model and the Fractal Ising model, both of which exhibit strongly first-order transitions into subsystem-ordered phases. Similar behavior is reviewed for other three-dimensional models with planar or fractal subsystem symmetries.

The authors emphasize that dimensional-reduction arguments constrain which subsystem symmetries can break but do not determine the order of the transition. Because continuous transitions are known to occur in some anisotropic limits and no general theorem enforces discontinuity, the existence of a genuine continuous transition in an isotropic, fully interacting model remains unresolved.