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 $c|x|<sup>{-(d-1)/2}$. The proof is based on the development in the random current representation of a "modern" Ornstein-Zernike theory, as developed by Campanino, Ioffe and Velenik.