Graph spectral characterization of the XY model on complex networks

Area of Science:

• Complex Systems
• Network Science
• Statistical Physics

Background:

• The XY spin model exhibits diverse macroscopic states influenced by network topology.
• Characterizing these states is crucial for understanding complex system dynamics.

Purpose of the Study:

• To develop a robust method for characterizing macroscopic states of the XY spin model.
• To utilize spectral decomposition of time series and network topology for state identification.

Main Methods:

• Generated time series data for the XY spin model on three network classes representing distinct macroscopic states.
• Applied the temporal Graph Signal Transform (tGST) for spectral decomposition of spin time series.
• Analyzed spatial power spectra derived from the decomposition to identify state signatures.

Main Results:

• Spatial power spectra revealed distinct patterns corresponding to the three macroscopic states.
• These spectral signatures were independent of the underlying network topology.
• The method successfully differentiated between the macroscopic states based on dynamic activity patterns.

Conclusions:

• Spectral decomposition of time series offers a robust and network-independent method to characterize XY spin model macroscopic states.
• Temporal Graph Signal Analysis provides powerful tools for analyzing complex network dynamics.
• This approach can be generalized for analyzing other complex systems on networks.