, Volume 125, Issue 3, pp 305-349

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.

Received: 10 January 2002 / Revised version: 19 June 2002 / Published online: 14 November 2002
Partly supported by Italian G. N. A. F. A, EC grant SC1-CT91-0695 and the University of Bologna. Funds for selected research topics.
Partly supported by the ISRAEL SCIENCE FOUNDATION founded by The Israel Academy of Science and Humanities.
Partly supported by the Swiss National Science Foundation grant #8220-056599.
Mathematics Subject Classification (2000): 60F15, 60K15, 60K35, 82B20, 37C30
Key words or phrases: Ising model – Ornstein-Zernike decay of correlations – Ruelle operator – Renormalization – Local limit theorems