Journal of Statistical Physics

, Volume 126, Issue 4–5, pp 1007–1024 | Cite as

Two Connections Between Random Systems and Non-Gibbsian Measures

  • Aernout C. D. van Enter
  • Christof Külske
Open Access


In this contribution we discuss the role disordered (or random) systems have played in the study of non-Gibbsian measures. This role has two main aspects, the distinction between which has not always been fully clear: 1) From disordered systems: Disordered systems can be used as a tool; analogies with, as well as results and methods from the study of random systems can be employed to investigate non-Gibbsian properties of a variety of measures of physical and mathematical interest. 2) Of disordered systems: Non-Gibbsianness is a property of various (joint) measures describing quenched disordered systems. We discuss and review this distinction and a number of results related to these issues. Moreover, we discuss the mean-field version of the non-Gibbsian property, and present some ideas how a Kac limit approach might connect the finite-range and the mean-field non-Gibbsian properties.


quenched disorder non-Gibbsian measures Kac limits 


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Copyright information

© Springer Science+Business Media, Inc. 2006

Authors and Affiliations

  1. 1.Centre for Theoretical PhysicsRijksuniversiteit GroningenGroningenThe Netherlands
  2. 2.Department of Mathematics and Computer ScienceRijksuniversiteit GroningenGroningenThe Netherlands

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