# Graph spectral characterization of the XY model on complex networks.

@article{Expert2017GraphSC,
title={Graph spectral characterization of the XY model on complex networks.},
author={Paul Expert and Sarah de Nigris and Taro Takaguchi and Renaud Lambiotte},
journal={Physical review. E},
year={2017},
volume={96 1-1},
pages={
012312
}
}
• Published 4 November 2016
• Computer Science
• Physical review. E
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…
9 Citations

## Figures and Tables from this paper

### Synchronization in network geometries with finite spectral dimension.

• Mathematics, Physics
Physical review. E
• 2019
The role of the spectral dimension in determining the synchronization properties of the Kuramoto model is explored and it is shown that the synchronized phase can only be thermodynamically stable for spectral dimensions above four and that phase entrainment of the oscillators canonly be found for spectral dimension greater than two.

### Networks of coadjoint orbits: From geometric to statistical mechanics

• Physics
Journal of Geometric Mechanics
• 2019
A class of network models with symmetry group $G$ that evolve as a Lie-Poisson system is derived from the framework of geometric mechanics, which generalises the classical Heisenberg model studied in

### NETWORKS OF COADJOINT ORBITS : FROM GEOMETRIC TO STATISTICAL MECHANICS To

A class of network models with symmetry group G that evolve as a LiePoisson system is derived from the framework of geometric mechanics, which generalises the classical Heisenberg model studied in

### Hyperharmonic analysis for the study of high-order information-theoretic signals

• Computer Science
Journal of Physics: Complexity
• 2021
This work combines methods from harmonic analysis and combinatorial topology to construct efficient representations of high-order information-theoretic signals, using the diagonalisation of a discrete version of the Laplace–de Rham operator to encode structural properties of the system.

### Free and freer XY models.

• Physics
Physical review. E
• 2020
Two versions of the XY model where the spins but also the interaction topology is allowed to change are studied, and exponents describing the magnetic ordering are mostly consistent with values of the mean-field theory of the standard XY model.

### Analyzing Collective Motion Using Graph Fourier Analysis

• Computer Science
• 2021
This work shows how the field of graph signal processing can be used to fuse the two approaches to analysis of swarms by collectively analyzing swarm properties using graph Fourier harmonics that respect the topological structure of the swarm.

### Complex networks with tuneable spectral dimension as a universality playground

• Materials Science, Mathematics
• 2021
The authors study a complex network model whose spectral dimension can be continuously tuned in the range ${d}_{s}\ensuremath{\in}[1,+\mathrm{\ensuremath{\infty}}]$. The disorder contribution to this

### Analysis of the low-temperature phase in the two-dimensional long-range diluted XY model

• Physics
Physical Review B
• 2019
The critical behaviour of statistical models with long-range interactions exhibits distinct regimes as a function of $\rho$, the power of the interaction strength decay. For $\rho$ large enough,

### Improving learning step in artificial intelligence with categorization

• Computer Science
2020 18th International Conference on Emerging eLearning Technologies and Applications (ICETA)
• 2020
The aim of this paper is to improve learning stage of machine learning by correcting data and filling missing features in records which should result in better final (predicting) step of machinelearning.

## References

SHOWING 1-10 OF 39 REFERENCES

### Internet tomography

• Computer Science
IEEE Signal Process. Mag.
• 2002
This article introduces the new field of network tomography, a field which it is believed will benefit greatly from the wealth of signal processing theory and algorithms.

### Chemical oscillations

• Physics
• 2006
A chemical reaction is usually thought of as coming together of reactant molecules to form products. The concentrations of initial components (reactants) decrease, and concentrations of products

### Unified Green's function retrieval by cross-correlation; connection with energy principles.

• Physics
Physical review. E, Statistical, nonlinear, and soft matter physics
• 2007
The general theory opens up new applications for the extraction of the Green's function from field correlations that include flow in porous media, quantum mechanics, and the recovery of the response of mechanical structures such as bridges.

### Stress partition and micro-structure in size-segregating granular flows. Physical Review E: Statistical, Nonlinear, and Soft Matter Physics

• Geology
• 2015
When a granular mixture involving grains of diﬀerent sizes is shaken, sheared, mixed, or left to ﬂow, grains tend to separate by sizes in a process known as size segregation. In this study, we

### On the emergence of the Green's function in the correlations of a diffuse field: pulse-echo using thermal phonons.

• Physics
Ultrasonics
• 2002
It is shown that a diffuse field is not devoid of phase information, but has a correlation function equal to the Green's function, and the cross-correlation between diffuse signals in two transducers is very nearly equal to an impulse applied to the other.

### Extracting the Green's function from the correlation of coda waves: a derivation based on stationary phase.

• R. Snieder
• Physics
Physical review. E, Statistical, nonlinear, and soft matter physics
• 2004
An alternative derivation of passive imaging of the ballistic wave that is not based on normal modes is presented, showing that the global requirement of the equipartitioning of normal modes can be relaxed to the local requirement that the scattered waves propagate on average isotropically near the receivers.

### Retrieving the elastodynamic Green's function of an arbitrary inhomogeneous medium by cross correlation.

• K. Wapenaar
• Geology, Mathematics
Physical review letters
• 2004
A correlation-type reciprocity theorem is used to show that the elastodynamic Green's function of any inhomogeneous medium (random or deterministic) can be retrieved from the cross correlation of two

### and a at

• Chemistry
The William Makepeace Thackeray Library
• 2018
The xishacorene natural products are structurally unique apolar diterpenoids that feature a bicyclo[3.3.1] framework. These secondary metabolites likely arise from the well-studied, structurally

### Chaos

or "What a lie", or "How could I have said so"? or demanded at once that she should be sent for. Yet, he never on one single occasion, before others, spoke to Mrs. Cox on the subject. The only

• 83
• 1974