title: Breaking of Ensemble Equivalence in Networks.
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, nonequivalence is determined by a different large-deviation behavior 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.
authors.affiliation: Lorentz Institute for Theoretical Physics, University of Leiden, Leiden, The Netherlands.|IMT Institute for Advanced Studies, P.zza S. Ponziano 6, 55100 Lucca, Italy.
authors.forename: Tiziano
authors.initials: T
authors.lastname: Squartini
authors.affiliation: Lorentz Institute for Theoretical Physics, University of Leiden, Leiden, The Netherlands.|Mathematical Institute, University of Leiden, Netherlands.
authors.forename: Joey
authors.initials: J
authors.lastname: de Mol
authors.affiliation: Mathematical Institute, University of Leiden, Netherlands.
authors.forename: Frank
authors.initials: F
authors.lastname: den Hollander
authors.forename: Diego
authors.initials: D
authors.lastname: Garlaschelli