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Network science: Ising states of matter
Hanlin Sun1,2, Rajat Kumar Panda3,4,5,6, Roberto Verdel3
1School of Mathematical Sciences, Queen Mary University of London, London E1 4NS, United Kingdom.
Physical Review. E
|June 22, 2024
Summary
Network science reveals complex organization in 2D Ising networks across phase transitions. These networks, analyzed via statistical and topological methods, encode crucial information about phases of matter.
Area of Science:
- Statistical physics
- Network science
- Machine learning
Background:
- Machine learning is increasingly used for unsupervised detection of phases of matter.
- The predictive power of network science for phase transitions remains underexplored.
Purpose of the Study:
- To characterize 2D Ising snapshot networks (IsingNets) across the phase transition.
- To explore the application of network science tools for understanding phases of matter.
Main Methods:
- Extracting IsingNets from Monte Carlo simulations of the 2D Ising model.
- Performing statistical, combinatorial, geometrical, and topological analyses of IsingNets.
- Utilizing persistent homology and spectral property analysis.
Main Results:
- IsingNets exhibit complex organization in both ferromagnetic and paramagnetic phases, deviating from null models.
- Percolation properties reflect symmetry below the critical temperature, with compact giant clusters identified via persistent homology.
- Broad degree distributions and significant correlations indicate IsingNets encode configuration space information.
Conclusions:
- Network science offers valuable insights into characterizing phases of matter.
- The described network analysis tools are applicable to diverse numerical and experimental data.
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