Emergence of a boundary-sensitive phase in hyperbolic Ising models

The introduction of spatial curvature leads to novel phases lying beyond the conventional Landau and topological order paradigms. In Ising models on hyperbolic lattices, the authors identify a boundary-sensitive bulk ordered phase that emerges between the ferromagnetic and paramagnetic regimes as the temperature increases. Using a symmetry-restricted corner transfer matrix renormalization group approach, they map here the complete phase diagram with transitions linked by a boundary-transforming Kramers--Wannier duality. Cayley tree limit calculations expose a sharp holographic correspondence between boundary and bulk correlation functions.