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Ensemble inequivalence in random graphs

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  • Barré, Julien
  • Gonçalves, Bruno

Abstract

We present a complete analytical solution of a system of Potts spins on a random k-regular graph in both the canonical and microcanonical ensembles, using the Large Deviation Cavity Method (LDCM). The solution is shown to be composed of three different branches, resulting in a non-concave entropy function. The analytical solution is confirmed with numerical Metropolis and Creutz simulations and our results clearly demonstrate the presence of a region with negative specific heat and, consequently, ensemble inequivalence between the canonical and microcanonical ensembles.

Suggested Citation

  • Barré, Julien & Gonçalves, Bruno, 2007. "Ensemble inequivalence in random graphs," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 386(1), pages 212-218.
    • Handle: RePEc:eee:phsmap:v:386:y:2007:i:1:p:212-218
    DOI: 10.1016/j.physa.2007.08.015
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    References listed on IDEAS

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    1. M. Mézard & G. Parisi, 2001. "The Bethe lattice spin glass revisited," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 20(2), pages 217-233, March.
    2. Ispolatov, I & Cohen, E.G.D, 2001. "On first-order phase transitions in microcanonical and canonical non-extensive systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 295(3), pages 475-487.
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