Skip to main content

Advertisement

SpringerLink
Log in
Menu
Find a journal Publish with us
Search
Cart
  1. Home
  2. Probability Theory and Related Fields
  3. Article
Ornstein-Zernike theory for finite range Ising models above T c
Download PDF
Download PDF
  • Published: March 2003

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

  • Massimo Campanino1,
  • Dmitry Ioffe2 &
  • Y van Velenik3 

Probability Theory and Related Fields volume 125, pages 305–349 (2003)Cite this article

  • 337 Accesses

  • 45 Citations

  • 3 Altmetric

  • Metrics details

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 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<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.

Download to read the full article text

Working on a manuscript?

Avoid the common mistakes

Author information

Authors and Affiliations

  1. Dipartimento di Matematica, Università di Bologna, piazza di Porta S. Donato 5, I-40126 Bologna, Italy. e-mail: campanin@dm.unibo.it, , , , , , IT

    Massimo Campanino

  2. Faculty of Industrial Engineering, Technion, Haifa 3200, Israel. e-mail: ieioffe@ie.technion.ac.il, , , , , , IL

    Dmitry Ioffe

  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.fr, , , , , , FR

    Y van Velenik

Authors
  1. Massimo Campanino
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Dmitry Ioffe
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Y van Velenik
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

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

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Campanino, M., Ioffe, D. & Velenik, Y. Ornstein-Zernike theory for finite range Ising models above T c . Probab. Theory Relat. Fields 125, 305–349 (2003). https://doi.org/10.1007/s00440-002-0229-z

Download citation

  • Issue Date: March 2003

  • DOI: https://doi.org/10.1007/s00440-002-0229-z

Share this article

Anyone you share the following link with will be able to read this content:

Sorry, a shareable link is not currently available for this article.

Provided by the Springer Nature SharedIt content-sharing initiative

Keywords

  • Phase Transition
  • Temperature Region
  • Exponential Decay
  • Inverse Correlation
  • Correlation Length
Download PDF

Working on a manuscript?

Avoid the common mistakes

Advertisement

Search

Navigation

  • Find a journal
  • Publish with us

Discover content

  • Journals A-Z
  • Books A-Z

Publish with us

  • Publish your research
  • Open access publishing

Products and services

  • Our products
  • Librarians
  • Societies
  • Partners and advertisers

Our imprints

  • Springer
  • Nature Portfolio
  • BMC
  • Palgrave Macmillan
  • Apress
  • Your US state privacy rights
  • Accessibility statement
  • Terms and conditions
  • Privacy policy
  • Help and support

167.114.118.210

Not affiliated

Springer Nature

© 2023 Springer Nature