Ornstein-Zernike Theory for the Finite Range Ising Model above Tc, Probab. Theory and Relat

Abstract. We derive a precise Ornstein-Zernike asymptotic formula for the de-cay of the two-point function 〈σ0σx〉β in the general context of finite range Ising type models on Zd. The proof relies in an essential way on the a-priori knowl-edge 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