Uniqueness and Global Markov Property for Euclidean Fields and Lattice Systems

  • Sergio Albeverio
  • Raphael Høegh-Krohn
Conference paper


We give the results and the ideas of the proof concerning the uniqueness of the Gibbs states, in the class of regular generalized random fields, for the Euclidean Sine-Gordon fields in two dimensions. We also discuss in the same way the proof of the global Markov property of these fields. Consequences and applications of these properties in the theory of random fields and quantum field theory are also shortly discussed. Finally we show how the same basic ideas give a proof of the global Markov property for lattice systems.


Random Field Gibbs Measure Markov Property Dirichlet Form Markov Field 
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/Wien 1980

Authors and Affiliations

  • Sergio Albeverio
    • 1
  • Raphael Høegh-Krohn
    • 2
  1. 1.Fakultät für MathematikUniversität BielefeldGeneral Republic of Germany
  2. 2.Matematisk InstituttUniversitetet i OsloNorway

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