Complex networks with tuneable spectral dimension as a universality playground

Year: 2021

Authors: Millan A.P., Gori G., Battiston F., Enss T., Defenu N.

Autors Affiliation: Vrije Univ Amsterdam, Dept Clin Neurophysiol, Amsterdam UMC, De Boelelaan 1117, Amsterdam, Netherlands; Amsterdam Neurosci, MEG Ctr, De Boelelaan 1117, Amsterdam, Netherlands; Heidelberg Univ, Inst Theoret Phys, D-69120 Heidelberg, Germany; Cent European Univ, Dept Network & Data Sci, H-1051 Budapest, Hungary; Swiss Fed Inst Technol, Inst Theoret Phys, Wolfgang Pauli Str 27, CH-8093 Zurich, Switzerland.

Abstract: 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.

Journal/Review: PHYSICAL REVIEW RESEARCH

Volume: 3 (2)      Pages from: 23015-1  to: 23015-12

More Information: The authors acknowledge fruitful discussions with F. Cescatti, M. Ibanez-Berganza, and A. Trombettoni during various stages of this work. This work is supported by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation), Project-ID No. 273811115 (SFB1225 ISOQUANT) and under Germany’s Excellence Strategy EXC2181/1-390900948 (the Heidelberg STRUCTURES Excellence Cluster). F.B. acknowledges partial support from the ERC Synergy Grant No. 810115 (DYNASNET). A.P.M. also acknowledges support from the European Cooperation in Science & Technology (COST action Grant No. CA15109) and from Z onMW (grant 95105006) and the Dutch Epilepsy Foundation, Project No. 95105006.
KeyWords: Mermin-wagner Theorem; Critical Exponents; Phase-transitions; Epidemic Processes; Spherical Model; Small-world; Renormalization; Fractals; Dynamics; Equation
DOI: 10.1103/PhysRevResearch.3.023015

Citations: 14
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