Graph spectral characterisation of the XY model on complex networks
File(s)
Published version
Author(s)
Expert, P
de Nigris, S
Takaguchi, T
Lambiotte, R
Type
Journal Article
Abstract
There is recent evidence that the XY spin model on complex networks can display three different macroscopic states in response to the topology of the network underpinning the interactions of the spins. In this work we present a way to characterize the macroscopic states of the XY spin model based on the spectral decomposition of time series using topological information about the underlying networks. We use three different classes of networks to generate time series of the spins for the three possible macroscopic states. We then use the temporal Graph Signal Transform technique to decompose the time series of the spins on the eigenbasis of the Laplacian. From this decomposition, we produce spatial power spectra, which summarize the activation of structural modes by the nonlinear dynamics, and thus coherent patterns of activity of the spins. These signatures of the macroscopic states are independent of the underlying network class and can thus be used as robust signatures for the macroscopic states. This work opens avenues to analyze and characterize dynamics on complex networks using temporal Graph Signal Analysis.
Date Issued
2017-07-11
Date Acceptance
2017-06-06
Citation
Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, 2017, 96
ISSN
1063-651X
Publisher
American Physical Society
Journal / Book Title
Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
Volume
96
Copyright Statement
© 2017 The Authors. Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.
Publication Status
Published
Article Number
012312