Ensemble inequivalence in a Blume-Capel model on long-range random networks

Levon Chakhmakhchyan, Tarcisio N. Teles, Stefano Ruffo

Published 2016-09-07Version 1

Ensemble inequivalence has been previously displayed only for long-range interacting systems with a 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 propose a Blume-Capel model defined on long-range random networks, which allows one to avoid such a rescaling. Namely, the proposed model has an extensive energy, which is however non-additive. Specifically, for long-range random networks pairs of sites are coupled with a probability that decays with the distance $r$ as $1/r^\delta$, and if $0 \leq \delta <1$ the surface energy of the system scales linearly with the network size, while for $\delta >1$ it is $O(1)$. By performing numerical simulations independently in the canonical and microcanonical ensembles, we show that a negative specific heat region is present within the microcanonical description of the model, in correspondence with a first-order phase transition within the canonical ensemble. This proves that ensemble inequivalence is a consequence of non-additivity rather than non-extensivity.