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Journal of Statistical Physics

, Volume 123, Issue 6, pp 1285–1310 | Cite as

Analyticity and Mixing Properties for Random Cluster Model with q >0 on ℤ d

  • Aldo Procacci
  • Benedetto Scoppola
Article

Abstract

We study the Random Cluster Model on ℤ d for p near either 0 or 1 and for all q > 0 and we prove by mean of cluster expansion methods the analyticity of the pressure and finite connectivities in both regimes. These results are valid also in the regime q < 1 and they imply that percolation probability is strictly less than 1.

Key Words

Random cluster model cluster expansion 

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Copyright information

© Springer Science+Business Media, Inc. 2006

Authors and Affiliations

  • Aldo Procacci
    • 1
  • Benedetto Scoppola
    • 2
  1. 1.Departamento de Matemática UFMGBelo HorizonteBrazil
  2. 2.Dipartimento di MatematicaUniversitá “Tor Vergata” di RomaRomaItaly

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