Ornstein-Zernike theory for finite range Ising models above T c
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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.
KeywordsPhase Transition Temperature Region Exponential Decay Inverse Correlation Correlation Length
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