TY - JOUR

T1 - Ensemble inequivalence and absence of quasi-stationary states in long-range random networks

AU - Chakhmakhchyan, L.

AU - Teles, T. N.

AU - Ruffo, S.

PY - 2017/6/8

Y1 - 2017/6/8

N2 - 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.

AB - 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.

KW - classical phase transitions

KW - numerical simulations

UR - http://www.scopus.com/inward/record.url?scp=85021629048&partnerID=8YFLogxK

U2 - 10.1088/1742-5468/aa73f1

DO - 10.1088/1742-5468/aa73f1

M3 - Article (Academic Journal)

AN - SCOPUS:85021629048

VL - 2017

JO - Journal of Statistical Mechanics: Theory and Experiment

JF - Journal of Statistical Mechanics: Theory and Experiment

SN - 1742-5468

IS - 6

M1 - 063204

ER -