Communications in Mathematical Physics

, Volume 62, Issue 1, pp 1–34 | Cite as

Phase transitions and reflection positivity. I. General theory and long range lattice models

  • Jürg Fröhlich
  • Robert Israel
  • Elliot H. Lieb
  • Barry Simon
Article

Abstract

We systematize the study of reflection positivity in statistical mechanical models, and thereby two techniques in the theory of phase transitions: the method ofinfrared bounds and the chessboard method of estimating contour probabilities in Peierls arguments. We illustrate the ideas by applying them to models with long range interactions in one and two dimensions. Additional applications are discussed in a second paper.

Keywords

Reflection Neural Network Phase Transition Statistical Physic Complex System 

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Copyright information

© Springer-Verlag 1978

Authors and Affiliations

  • Jürg Fröhlich
    • 2
  • Robert Israel
    • 1
  • Elliot H. Lieb
    • 2
  • Barry Simon
    • 2
  1. 1.Department of MathematicsUniversity of British ColumbiaVancouverCanada
  2. 2.Departments of Mathematics and PhysicsPrinceton UniversityPrincetonUSA

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