Sharp Asymptotics for the Truncated Two-Point Function of the Ising Model with a Positive Field

Abstract

We prove that the correction to exponential decay of the truncated two points function in the homogeneous positive field Ising model is $$c\Vert x\Vert ^{-(d-1)/2}$$. The proof is based on the development in the random current representation of a “modern” Ornstein–Zernike theory, as developed by Campanino et al. (Ann Probab 36(4):1287–1321, 2008).