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.

Ensemble inequivalence and absence of quasi-stationary states in long-range random networks / Chakhmakhchyan, L.; Teles, T. N.; Ruffo, S.. - In: JOURNAL OF STATISTICAL MECHANICS: THEORY AND EXPERIMENT. - ISSN 1742-5468. - 2017:6(2017), p. 063204. [10.1088/1742-5468/aa73f1]

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

Ruffo S.
2017-01-01

Abstract

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.
2017
6
063204
063204
https://iopscience.iop.org/article/10.1088/1742-5468/aa73f1/meta
https://arxiv.org/abs/1609.02054
Chakhmakhchyan, L.; Teles, T. N.; Ruffo, S.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11767/116513
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