Ensemble inequivalence and absence of quasi-stationary states in long-range random networks

L. Chakhmakhchyan*, T. N. Teles, S. Ruffo

*Corresponding author for this work

Research output: Contribution to journalArticle (Academic Journal)peer-review

1 Citation (Scopus)


Ensemble inequivalence has been previously displayed only for long-range interacting systems with non-extensive energy. In order to perform the thermodynamic limit, such systems require an unphysical, so-called, Kac rescaling of the coupling constant. We here study models defined on long-range random networks, which avoid such a rescaling. The proposed models have an extensive energy, which is however non-additive. For such long-range random networks, pairs of sites are coupled with a probability decaying with the distance r as . In one dimension and with , the surface energy scales linearly with the network size, while for it is O(1). By performing numerical simulations, we show that a negative specific heat region is present in the microcanonical ensemble of a Blume-Capel model, in correspondence with a first-order phase transition in the canonical one. This proves that ensemble inequivalence is a consequence of non-additivity rather than non-extensivity. Moreover, since a mean-field coupling is absent in such networks, relaxation to equilibrium takes place on an intensive time scale and quasi-stationary states are absent.

Original languageEnglish
Article number063204
JournalJournal of Statistical Mechanics: Theory and Experiment
Issue number6
Publication statusPublished - 8 Jun 2017


  • classical phase transitions
  • numerical simulations


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