2002/09/16 by Julien Barré, Julien Barre', Barre', Julien +4 · 1 citation
Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Statistical Mechanics and Entropy #Theoretical and Computational Physics #cond-mat.stat-mech
paper · pdf · doi:10.48550/arxiv.cond-mat/0209357
Chapter of the forthcoming "Lecture Notes in Physics" volume: ``Dynamics and Thermodynamics of Systems with Long Range Interactions'', T. Dauxois, S. Ruffo, E. Arimondo, M. Wilkens Eds., Lecture Notes in Physics Vol. 602, Springer (2002). (see http://link.springer.de/series/lnpp/)
Mean-field models, while they can be cast into an \it extensive thermodynamic formalism, are inherently \it non additive. This is the basic feature which leads to \it 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 \it canonical and in the \it 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.