Renormalization-group description of boundary-flow universality

Develop a renormalization-group description of the boundary flow governing how thermodynamic boundary conditions select critical scaling on non-amenable hyperbolic lattices.

Background

The paper studies the ferromagnetic Ising model on finite hyperbolic tessellations with open and wired boundary conditions. Because hyperbolic lattices are non-amenable, their boundaries contain an extensive fraction of the sites, so boundary dynamics can affect the thermodynamic limit rather than acting as a subleading perturbation.

Open boundary conditions retain independent boundary fluctuations and produce non-mean-field finite-size-scaling exponents, whereas wired boundary conditions suppress those fluctuations through a collective auxiliary spin and yield mean-field-like critical behavior. The authors interpret these results as evidence that boundary conditions may form part of the definition of a universality class. A corresponding theoretical renormalization-group framework describing the flow between such boundary conditions and the associated critical theories is explicitly identified as unresolved.