Ornstein-Zernike theory for finite range Ising models above Tc

Abstract

We derive a precise Ornstein-Zernike asymptotic formula for the decay of the two-point function 〈σ0σx〉β in the general context of unite range Ising type models on ℤd. The proof relies in an essential way on the a-priori knowledge of the strict exponential decay of the two-point function and by the sharp characterization of phase transition due to Aizenman, Barsky and Fernández, goes through in the whole of the high temperature region β < βc. As a byproduct we obtain that for every β < βc, the inverse correlation length ξβ is an analytic and strictly convex function of direction.