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Complex networks with tuneable spectral dimension as a universality playground

Universality is one of the key concepts in understanding critical phenomena. However, for interacting inhomogeneous systems described by complex networks, a clear understanding of the relevant parameters for universality is still missing. Here we discuss the role of a fundamental network parameter f...

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Bibliographic Details
Main Authors: Millán, Ana P. (Author) , Gori, Giacomo (Author) , Battistoni, Federico (Author) , Enss, Tilman (Author) , Defenu, Nicolò (Author)
Format: Article (Journal)
Language:English
Published: 5 April 2021
In: Physical review research
Year: 2021, Volume: 3, Issue: 2, Pages: 1-12
ISSN:2643-1564
DOI:10.1103/PhysRevResearch.3.023015
Online Access:Verlag, lizenzpflichtig, Volltext: https://doi.org/10.1103/PhysRevResearch.3.023015
Verlag, lizenzpflichtig, Volltext: https://link.aps.org/doi/10.1103/PhysRevResearch.3.023015
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Author Notes:Ana P. Millán, Giacomo Gori, Federico Battiston, Tilman Enss and Nicolò Defenu
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Summary:Universality is one of the key concepts in understanding critical phenomena. However, for interacting inhomogeneous systems described by complex networks, a clear understanding of the relevant parameters for universality is still missing. Here we discuss the role of a fundamental network parameter for universality, the spectral dimension. For this purpose, we construct a complex network model where the probability of a bond between two nodes is proportional to a power law of the nodes' distances. By explicit computation we prove that the spectral dimension for this model can be tuned continuously from 1 to infinity, and we discuss related network connectivity measures. We propose our model as a tool to probe universal behavior on inhomogeneous structures and comment on the possibility that the universal behavior of correlated models on such networks mimics the one of continuous field theories in fractional Euclidean dimensions.
Item Description:Gesehen am 14.09.2022
Physical Description:Online Resource
ISSN:2643-1564
DOI:10.1103/PhysRevResearch.3.023015

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