Ensemble Inequivalence in Mean-Field Models of Magnetism View Full Text


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Chapter Info

DATE

2002-12-18

AUTHORS

Julien Barré , David Mukamel , Stefano Ruffo

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. More... »

PAGES

45-67

References to SciGraph publications

  • 2002-12-18. The Hamiltonian Mean Field Model: From Dynamics to Statistical Mechanics and Back in DYNAMICS AND THERMODYNAMICS OF SYSTEMS WITH LONG-RANGE INTERACTIONS
  • 1998. Large Deviations Techniques and Applications in NONE
  • 1969-06. Existence of a phase-transition in a one-dimensional Ising ferromagnet in COMMUNICATIONS IN MATHEMATICAL PHYSICS
  • 1970-08. Systems with negative specific heat in ZEITSCHRIFT FÜR PHYSIK A HADRONS AND NUCLEI
  • 2000-12. Large Deviation Principles and Complete Equivalence and Nonequivalence Results for Pure and Mixed Ensembles in JOURNAL OF STATISTICAL PHYSICS
  • 2002-12-18. Phase Transitions in Finite Systems in DYNAMICS AND THERMODYNAMICS OF SYSTEMS WITH LONG-RANGE INTERACTIONS
  • 2002-12-18. Phase Transitions in Systems with 1/rα Attractive Interactions in DYNAMICS AND THERMODYNAMICS OF SYSTEMS WITH LONG-RANGE INTERACTIONS
  • 2002. Nonextensivity: From Low-Dimensional Maps to Hamiltonian Systems in DYNAMICS AND THERMODYNAMICS OF SYSTEMS WITH LONG-RANGE INTERACTIONS
  • 2002-12-18. Statistical Mechanics of Gravitating Systems in Static and Cosmological Backgrounds in DYNAMICS AND THERMODYNAMICS OF SYSTEMS WITH LONG-RANGE INTERACTIONS
  • 2002-12-18. Statistical Mechanics of Two-Dimensional Vortices and Stellar Systems in DYNAMICS AND THERMODYNAMICS OF SYSTEMS WITH LONG-RANGE INTERACTIONS
  • Book

    TITLE

    Dynamics and Thermodynamics of Systems with Long-Range Interactions

    ISBN

    978-3-540-44315-5
    978-3-540-45835-7

    Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/3-540-45835-2_3

    DOI

    http://dx.doi.org/10.1007/3-540-45835-2_3

    DIMENSIONS

    https://app.dimensions.ai/details/publication/pub.1001298972


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