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Journal of Statistical Physics

, Volume 55, Issue 1–2, pp 171–181 | Cite as

Non-Gibbsian limit for large-block majority-spin transformations

  • T. C. Dorlas
  • A. C. D. van Enter
Articles

Abstract

We generalize a result of Lebowitz and Maes, that projections of massless Gaussian measures onto Ising spin configurations are non-Gibbs measures. This result provides the first evidence for the existence of singularities in majority-spin transformations of critical models. Indeed, under the assumption of the folk theorem that an average-block-spin transformation applied to a critical Ising model in 5 or more dimensions converges to a Gaussian fixed point, we show that the limit of a sequence of majority-spin transformations with increasing block size applied to a critical Ising model is a measure that is not of Gibbsian type.

Key words

Non-Gibbs measure real-space renormalization 

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Copyright information

© Plenum Publishing Corporation 1989

Authors and Affiliations

  • T. C. Dorlas
    • 1
  • A. C. D. van Enter
    • 2
  1. 1.Dublin Institute for Advanced StudiesDublin 4Ireland
  2. 2.Lady Davis Fellow, Department of PhysicsTechnionHaifaIsrael

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