Fractal Fluctuations at Mixed-Order Transitions in Interdependent Networks

Bnaya Gross, Ivan Bonamassa, Shlomo Havlin

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9 Scopus citations

Abstract

We study the critical features of the order parameter's fluctuations near the threshold of mixed-order phase transitions in randomly interdependent spatial networks. Remarkably, we find that although the structure of the order parameter is not scale invariant, its fluctuations are fractal up to a well-defined correlation length ζ′ that diverges when approaching the mixed-order transition threshold. We characterize the self-similar nature of these critical fluctuations through their effective fractal dimension df′=3d/4, and correlation length exponent ν′=2/d, where d is the dimension of the system. By analyzing percolation and magnetization, we demonstrate that df′ and ν′ are the same for both, i.e., independent of the symmetry of the process for any d of the underlying networks.

Original languageEnglish
Article number268301
JournalPhysical Review Letters
Volume129
Issue number26
DOIs
StatePublished - 23 Dec 2022

Bibliographical note

Publisher Copyright:
© 2022 American Physical Society.

Funding

We thank the Israel Science Foundation, the NSF-BSF Grant No. 2019740, the EU H2020 project RISE (Project No. 821115) and the EU H2020 DIT4TRAM for financial support.

FundersFunder number
EU H2020821115
EU H2020 DIT4TRAM
NSF-BSF2019740
Israel Science Foundation

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