BOUNDARY CORRELATION FUNCTIONS FOR NON EXACTLY SOLVABLE CRITICAL ISING MODELS.

Abstract

e consider a class of non exactly solvable Ising models in two dimen sions, whose Hamiltonian, in addition to the standard nearest neighbor cou plings, includes additional weak multi-spin interactions which are even under spin flip. We study the model in the upper half plane and compute the two point boundary spin correlations at the critical temperature in terms of a multiscale expansion. We prove that, in the scaling limit, the correlations converge to the same limiting correlations as those of the exactly solvable Ising model with renormalized critical temperature and renormalized wave functions. The proof is based on a representation of the generating function of correlations in terms of a non-Gaussian Grassmann integral, and a con structive Renormalization Group (RG) analysis thereof, enhanced by new technical results on the systematic analysis of the effect of the boundary corrections to the RG flow.