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Phase Transitions and Critical Points

  • James Glimm
  • Arthur Jaffe

Abstract

For statistical behavior in a family ξ i of random variables, we required in Chapter 2 the property of almost independence: ξ i should be almost independent of all but a finite number of ξ j . This property, in the sense of short range stable forces, was satisfied by the examples of Chapter 2. We now draw a further distinction of weak vs. strong interactions. Weak means that ξ i should be almost independent of all ξ j , ji, while strong means that ξ i is strongly correlated to a finite number of ξ j , j ≠ i. The weak coupling situations are handled by expansions, as in Chapter 2, and should be regarded as perturbations of an infinite tensor product, zero interaction model.

Keywords

Phase Transition Ising Model Cluster Expansion Droplet Model Dimensional Ising Model 
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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References

  1. [Domb and Green, 1972-], [Ruelle, 1969], [Stanley, 1971].Google Scholar

Copyright information

© Springer-Verlag New York Inc. 1987

Authors and Affiliations

  • James Glimm
    • 1
  • Arthur Jaffe
    • 2
  1. 1.Courant Institute for Mathematical SciencesNew York UniversityNew YorkUSA
  2. 2.Harvard UniversityCambridgeUSA

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