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Probability Theory and Related Fields

, Volume 125, Issue 3, pp 305–349 | Cite as

Ornstein-Zernike theory for finite range Ising models above T c

  • Massimo Campanino
  • Dmitry Ioffe
  • Y van Velenik

Abstract.

 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.

Keywords

Phase Transition Temperature Region Exponential Decay Inverse Correlation Correlation Length 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Massimo Campanino
    • 1
  • Dmitry Ioffe
    • 2
  • Y van Velenik
    • 3
  1. 1.Dipartimento di Matematica, Università di Bologna, piazza di Porta S. Donato 5, I-40126 Bologna, Italy. e-mail: campanin@dm.unibo.itIT
  2. 2.Faculty of Industrial Engineering, Technion, Haifa 3200, Israel. e-mail: ieioffe@ie.technion.ac.ilIL
  3. 3.Laboratoire d'Analyse, Topologie et Probabilités, UMR-CNRS 6632, CMI, Université de Provence, 39 rue Joliot Curie, 13453 Marseille, France. e-mail: velenik@cmi.univ-mrs.frFR

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