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
Large deviations and continuum limit in the 2D Ising model
Download PDF
Download PDF
  • Article
  • Published: November 1997

Large deviations and continuum limit in the 2D Ising model

  • C.-E. Pfister1 &
  • Y. Velenik1 

Probability Theory and Related Fields volume 109, pages 435–506 (1997)Cite this article

  • 199 Accesses

  • 42 Citations

  • Metrics details

Summary.

We study the 2D Ising model in a rectangular box Λ L of linear size O(L). We determine the exact asymptotic behaviour of the large deviations of the magnetization ∑ t∈ΛL σ(t) when L→∞ for values of the parameters of the model corresponding to the phase coexistence region, where the order parameter m * is strictly positive. We study in particular boundary effects due to an arbitrary real-valued boundary magnetic field. Using the self-duality of the model a large part of the analysis consists in deriving properties of the covariance function <σ(0)σ(t)>, as |t|→∞, at dual values of the parameters of the model. To do this analysis we establish new results about the high-temperature representation of the model. These results are valid for dimensions D≥2 and up to the critical temperature. They give a complete non-perturbative exposition of the high-temperature representation.

We then study the Gibbs measure conditioned by {|∑ t∈ΛL σ(t) −m|Λ L ||≤|Λ L |L − c}, with 0<c<1/4 and −m *<m<m *. We construct the continuum limit of the model and describe the limit by the solutions of a variational problem of isoperimetric type.

Download to read the full article text

Working on a manuscript?

Avoid the common mistakes

Author information

Authors and Affiliations

  1. Département de Mathématiques, EPF-L, CH-1015 Lausanne, Switzerland e-mail: cpfister@eldp.epfl.ch; velenik@eldp.epfl.ch, , , , , , CH

    C.-E. Pfister & Y. Velenik

Authors
  1. C.-E. Pfister
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Y. Velenik
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Received: 17 October 1996 / In revised form: 7 March 1997

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Pfister, CE., Velenik, Y. Large deviations and continuum limit in the 2D Ising model. Probab Theory Relat Fields 109, 435–506 (1997). https://doi.org/10.1007/s004400050139

Download citation

  • Issue Date: November 1997

  • DOI: https://doi.org/10.1007/s004400050139

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

  • AMS Subject Classification: (1991) 60F10
  • 60G60
  • 60K35
  • 82B20
  • 82B24
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