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Communications in Mathematical Physics

, Volume 327, Issue 3, pp 951–991 | Cite as

One-Dimensional Ising Models with Long Range Interactions: Cluster Expansion, Phase-Separating Point

  • Marzio Cassandro
  • Immacolata Merola
  • Pierre Picco
  • Utkir Rozikov
Article

Abstract

We consider the phase separation problem for the one-dimensional ferromagnetic Ising model with long-range two-body interaction, J(n) = n −2+α , where \({n\in {\rm {I\!N}}}\) denotes the distance of the two spins and \({\alpha \in [0,\alpha_+[}\) with α + = (log 3)/(log 2) −1. We prove that when α = 0 the localization of the phase separation fluctuates macroscopically with a non-uniform explicit limiting law, while when 0 < α < α + the macroscopic fluctuations disappear and mesoscopic ones appear with a gaussian behavior when conveniently scaled. The mean magnetization profile is also given.

Keywords

Ising Model Range Interaction Gibbs State Cluster Expansion External Contour 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Marzio Cassandro
    • 1
  • Immacolata Merola
    • 2
  • Pierre Picco
    • 3
  • Utkir Rozikov
    • 4
  1. 1.Gran Sasso Science Institute, INFN Center for Advanced StudiesL’AquilaItaly
  2. 2.Dipartimento di MatematicaUniversità di L’AquilaCoppito (AQ)Italy
  3. 3.LATP, CMI, UMR 6632, CNRS, Université de ProvenceMarseille Cedex 13France
  4. 4.Institute of MathematicsTashkentUzbekistan

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