Journal of Statistical Physics

, Volume 157, Issue 3, pp 407–421 | Cite as

Phase Transitions in Layered Systems

  • Luiz Renato Fontes
  • Domingos H. U. Marchetti
  • Immacolata Merola
  • Errico Presutti
  • Maria Eulalia Vares


We consider the Ising model on \(\mathbb Z\times \mathbb Z\) where on each horizontal line \(\{(x,i), x\in \mathbb Z\}\), called “layer”, the interaction is given by a ferromagnetic Kac potential with coupling strength \(J_{ \gamma }(x,y)={ \gamma }J({ \gamma }(x-y))\), where \(J(\cdot )\) is smooth and has compact support; we then add a nearest neighbor ferromagnetic vertical interaction of strength \({ \gamma }^{A}\), where \(A\ge 2\) is fixed, and prove that for any \(\beta \) larger than the mean field critical value there is a phase transition for all \({ \gamma }\) small enough.


Kac potentials Phase transitions Peierls estimates 

Mathematics Subject Classification

60K35 82B20 



MEV thanks the warm hospitality of GSSI, L’Aquila, where part of this research was done. Research partially supported by CNPq Grant 474233/2012-0. MEV’s work is partially supported by CNPq Grant 304217/2011-5 and Faperj Grant E-24/2013-132035. LRF’s work is partially supported by CNPq Grant 305760/2010-6 and Fapesp Grant 2009/52379-8.


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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  • Luiz Renato Fontes
    • 1
  • Domingos H. U. Marchetti
    • 2
  • Immacolata Merola
    • 3
  • Errico Presutti
    • 4
  • Maria Eulalia Vares
    • 5
  1. 1.Instituto de Matemática e EstatísticaUniversidade de São PauloSão PauloBrazil
  2. 2.Instituto de FísicaUniversidade de São PauloSão PauloBrazil
  3. 3.DISIMUniversità di L’AquilaL’AquilaItaly
  4. 4.GSSIL’AquilaItaly
  5. 5.Instituto de MatemáticaUniversidade Federal do Rio de JaneiroRio de JaneiroBrazil

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