Journal of Statistical Physics

, Volume 161, Issue 1, pp 91–122 | Cite as

Layered Systems at the Mean Field Critical Temperature

  • 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 \(\{(x,i), x\in \mathbb Z\}\) the interaction is given by a ferromagnetic Kac potential with coupling strength \(J_{ \gamma }(x,y)\sim \gamma J(\gamma (x-y))\) at the mean field critical temperature. We then add a nearest neighbor ferromagnetic vertical interaction of strength \(\epsilon \) and prove that for every \(\epsilon >0\) the systems exhibits phase transition provided \(\gamma >0\) is small enough.


Kac potentials Lebowitz–Penrose free energy functional Phase transition 

Mathmatics 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 2015

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.DISIM, Università di L’AquilaL’AquilaItaly
  4. 4.GSSIL’AquilaItaly
  5. 5.Instituto de MatemáticaUniversidade Federal do Rio de JaneiroRio de JaneiroBrazil

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