Random-Cluster Correlation Inequalities for Gibbs Fields

  • Alberto Gandolfi


In this note we prove a correlation inequality for local variables of a Gibbs field based on the connectivity in a random cluster representation of the non overlap configuration distribution of two independent copies of the field. As a consequence, we show that absence of a particular type of percolation (of Machta–Newman–Stein blue bonds) implies uniqueness of Gibbs distribution in EA Spin Glasses. In dimension two this could constitute a step towards a proof that the critical temperature is zero.


Correlation inequalities Gibbs fields Random cluster representation Disagreement percolation Spin glasses 

Mathematics Subject Classification

60G60 60J99 82B44 82D30 


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© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Science divisionNYU Abu DhabiAbu DhabiUnited Arab Emirates
  2. 2.Dipartimento di Matematica e Informatica U. DiniUniversità di FirenzeFirenzeItaly

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