Abstract

In the last few years, the methods of constructive fermionic Renormalization Group have successfully been applied to the study of the scaling limit of several 2D statistical mechanics models at the critical point, including the 2D Ising with finite range interactions. Different instances of universality have been proved in these context, including the facts that the scaling limit of the bulk energy-energy correlations and the central charge (computed from the leading sub-leading contribution to the critical free energy) are independent of the interaction. More recently, we extended our constructive RG method to the study of more subtle finite size observables: I will report ongoing progress on the scaling limit of the energy correlations in finite domains, and on the computation of the modular-invariant function associated with the sub-leading contribution to the critical free energy. Our methods may be relevant in a more general context for the study of the flow of the effective boundary conditions in critical models in a finite domain.
Based on joint work with V. Mastropietro, R. Greenblatt and G. Antinucci.