The scaling limit of boundary spin correlations in non-integrable Ising models

Abstract: We consider a class of non-integrable planar Ising models obtained by perturbing the nearest-neighbor model via a weak, finite range potential which preserves translation and spin-flip symmetry, and we study its critical theory in the half-plane. We prove that the scaling limit of the multipoint boundary spin correlations is the same as for the nearest-neighbor model, up to an analytic multiplicative renormalization constant. The proof is based on an exact representation of the generating function of correlations in terms of a Grassmann integral and on a multiscale analysis thereof, generalizing previous results to include observables located on the boundary. This is a joint work with A. Giuliani (Università degli Studi Roma Tre) and R.L. Greenblatt (Università degli Studi di Roma Tor Vergata).