On the absence of phase transition in one-dimensional random fields

I. Sufficient conditions
  • F. Papangelou
Article
  • 33 Downloads

Summary

Sufficient conditions are given for a one-dimensional random field specification (system of conditional distributions) to admit at most one unconditional distribution within a specified class of such distributions. The proof of the main result is based on a limit theorem on the asymptotic behaviour of the specification in relation to the field, which expresses the weak dependence of the conditional distributions on distant sites. In a subsequent article the results are applied to a class of superstable spin systems with long range interaction.

Keywords

Phase Transition Probability Measure Random Field Conditional Distribution Tame 

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Copyright information

© Springer-Verlag 1984

Authors and Affiliations

  • F. Papangelou
    • 1
  1. 1.Department of MathematicsThe UniversityManchesterUK

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