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Ensemble Inequivalence in Mean-Field Models of Magnetism

  • Julien Barré
  • David Mukamel
  • Stefano Ruffo
Chapter
Part of the Lecture Notes in Physics book series (LNP, volume 602)

Abstract

Mean-field models, while they can be cast into an extensive thermodynamic formalism, are inherently non additive. This is the basic feature which leads to ensemble inequivalence in these models. In this paper we study the global phase diagram of the infinite range Blume-Emery-Griffiths model both in the canonical and in the microcanonical ensembles. The microcanonical solution is obtained both by direct state counting and by the application of large deviation theory. The canonical phase diagram has first order and continuous transition lines separated by a tricritical point. We find that below the tricritical point, when the canonical transition is first order, the phase diagrams of the two ensembles disagree. In this region the microcanonical ensemble exhibits energy ranges with negative specific heat and temperature jumps at transition energies. These two features are discussed in a general context and the appropriate Maxwell constructions are introduced. Some preliminary extensions of these results to weakly decaying nonintegrable interactions are presented.

Keywords

Ising Model Order Transition Order Phase Transition Canonical Ensemble Short Range Interaction 
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 2002

Authors and Affiliations

  • Julien Barré
    • 1
    • 3
  • David Mukamel
    • 2
  • Stefano Ruffo
    • 1
    • 3
  1. 1.Laboratoire de PhysiqueEcole Normale Supérieure de LyonLyon Cedex 07France
  2. 2.Department of Physics of Complex SystemsThe Weizmann Institute of ScienceRehovotIsrael
  3. 3.Dipartimento di Energetica “Sergio Stecco”Università di Firenze, INFM and INFNFirenzeItaly

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