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Communications in Mathematical Physics

, Volume 122, Issue 4, pp 597–607 | Cite as

A note on the Ising model in high dimensions

  • J. Bricmont
  • H. Kesten
  • J. L. Lebowitz
  • R. H. Schonmann
Article

Abstract

We consider thed-dimensional Ising model with a nearest neighbor ferromagnetic interactionJ(d)=1/4d. We show that asd→∞ the+phase (and the — phase) approaches a product measure with density given by the mean field approximation. In particular the spontaneous magnetization converges to its mean field value. A similar result holds for the unique Gibbs measure of the system subject to an external fieldh≠0.

Keywords

Neural Network Statistical Physic Complex System Nonlinear Dynamics High Dimension 
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 1989

Authors and Affiliations

  • J. Bricmont
    • 1
  • H. Kesten
    • 2
  • J. L. Lebowitz
    • 3
  • R. H. Schonmann
    • 2
  1. 1.Institut de Physique TheoriqueUniversite Catholique de LouvainLouvain-la-NeuveBelgium
  2. 2.Department of Mathematics, White HallCornell UniversityIthacaUSA
  3. 3.Department of MathematicsRutgers UniversityNew BrunswickUSA

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