Ornstein-Zernike theory for finite range Ising models above T c
- Cite this article as:
- Campanino, M., Ioffe, D. & Velenik, Y. Probab. Theory Relat. Fields (2003) 125: 305. doi:10.1007/s00440-002-0229-z
We derive a precise Ornstein-Zernike asymptotic formula for the decay of the two-point function 〈Σ0Σ x 〉β in the general context of finite range Ising type models on ℤ d . 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<β c . As a byproduct we obtain that for every β<β c , the inverse correlation length ξβ is an analytic and strictly convex function of direction.