Ornstein-Zernike theory for finite range Ising models above Tc
- Cite this article as:
- Campanino, M., Ioffe, D. & Velenik, Y. Probab. Theory Relat. Fields (2003) 125: 305. doi:10.1007/s00440-002-0229-z
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We derive a precise Ornstein-Zernike asymptotic formula for the decay 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 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.