eprintid: 2835
rev_number: 9
eprint_status: archive
userid: 69
dir: disk0/00/00/28/35
datestamp: 2015-11-05 15:04:15
lastmod: 2018-03-08 16:57:32
status_changed: 2015-11-05 15:04:15
type: article
metadata_visibility: show
creators_name: Squartini, Tiziano
creators_name: de Mol, Joey
creators_name: Hollander, Frank den
creators_name: Garlaschelli, Diego
creators_id: tiziano.squartini@imtlucca.it
creators_id: 
creators_id: 
creators_id: diego.garlaschelli@imtlucca.it
title: Breaking of ensemble equivalence in networks
ispublished: submitted
subjects: QA
subjects: QC
divisions: EIC
full_text_status: public
abstract: It is generally believed that, in the thermodynamic limit, the microcanonical description as a function of energy coincides with the canonical description as a function of temperature. However, various examples of systems for which the microcanonical and canonical ensembles are not equivalent have been identified. A complete theory of this intriguing phenomenon is still missing. Here we show that ensemble nonequivalence can manifest itself also in random graphs with topological constraints. We find that, while graphs with a given number of links are ensemble-equivalent, graphs with a given degree sequence are not. This result holds irrespective of whether the energy is nonadditive (as in unipartite graphs) or additive (as in bipartite graphs). In contrast with previous expectations, our results show that: (1) physically, nonequivalence can be induced by an extensive number of local constraints, and not necessarily by long-range interactions or nonadditivity; (2) mathematically, nonquivalence is determined by a different large-deviation behaviour of microcanonical and canonical probabilities for a single microstate, and not necessarily for almost all microstates. The latter criterion, which is entirely local, is not restricted to networks and holds in general
date: 2015
date_type: submitted
publication: Physical Review Letters
publisher: American Physical Society
refereed: TRUE
issn: 0031-9007
citation:   Squartini, Tiziano and de Mol, Joey and Hollander, Frank den and Garlaschelli, Diego  Breaking of ensemble equivalence in networks.  Physical Review Letters.   ISSN 0031-9007    (Submitted)   (2015)  
document_url: http://eprints.imtlucca.it/2835/1/1501.00388v4.pdf