Journal of Statistical Physics

, Volume 83, Issue 3–4, pp 761–765 | Cite as

Ill-defined block-spin transformations at arbitrarily high temperatures

  • Aernout C. D. van Enter
Short Communications


Examples are presented of block-spin transformations which map the Gibbs measures of the Ising model in two or more dimensions at temperature intervals extending to arbitrarily high temperatures onto non-Gibbsian measures. In this way we provide the first example of this kind of pathology for very high temperatures, and as a corollary also the first example of such a pathology happening at a critical point.

Key Words

Non-Gibbsian measures block-spin map pathology 


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Copyright information

© Plenum Publishing Corporation 1996

Authors and Affiliations

  • Aernout C. D. van Enter
    • 1
  1. 1.Institute for Theoretical PhysicsRijksuniversiteit GroningenGroningenThe Netherlands

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