Probability Theory and Related Fields

, Volume 125, Issue 3, pp 305–349

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

Authors

  • Massimo Campanino
    • Dipartimento di Matematica, Università di Bologna, piazza di Porta S. Donato 5, I-40126 Bologna, Italy. e-mail: campanin@dm.unibo.it
  • Dmitry Ioffe
    • Faculty of Industrial Engineering, Technion, Haifa 3200, Israel. e-mail: ieioffe@ie.technion.ac.il
  • Y van Velenik
    • 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.fr

DOI: 10.1007/s00440-002-0229-z

Cite this article as:
Campanino, M., Ioffe, D. & Velenik, Y. Probab. Theory Relat. Fields (2003) 125: 305. doi:10.1007/s00440-002-0229-z

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.

Copyright information

© Springer-Verlag Berlin Heidelberg 2003