Journal of Statistical Physics

, Volume 122, Issue 1, pp 59–72 | Cite as

Slab Percolation and Phase Transitions for the Ising Model

  • Emilio De Santis
  • Rossella Micieli


We prove, using the random-cluster model, a strict inequality between site percolation and magnetization in the region of phase transition for the d-dimensional Ising model, thus improving a result of [5]. We extend this result also at the case of two plane lattices \({\mathbb Z}\) (slabs) and give a characterization of phase transition in this case. The general case of N slabs, with N an arbitrary positive integer, is partially solved and it is used to show that this characterization holds in the case of three slabs with periodic boundary conditions.

Key Words

Percolation infinite clusters magnetization Gibbs measure random-cluster measure 


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Copyright information

© Springer Science + Business Media, Inc. 2006

Authors and Affiliations

  1. 1.Dipartimento di Matematica “Guido Castelnuovo”Università di Roma “La Sapienza”.RomaItalia

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