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Persistent homology analysis of phase transitions
Irene Donato1, Matteo Gori1, Marco Pettini1
1Aix-Marseille University, CNRS Centre de Physique Théorique UMR 7332, Campus de Luminy, Case 907, 13288 Marseille Cedex 09, France.
Physical Review. E
|June 15, 2016
Summary
Persistent homology analysis successfully identified phase transitions in physical models. This computational topology method accurately captured known topological properties of configuration spaces.
Area of Science:
- Computational topology
- Algebraic topology
- Statistical mechanics
Background:
- Phase transitions are critical phenomena in physical systems.
- Understanding the topology of configuration space is key to characterizing phase transitions.
- Traditional methods may not fully capture the complex topological features related to phase transitions.
Purpose of the Study:
- To apply persistent homology analysis to study phase transitions in physical models.
- To investigate the relationship between topological properties and phase transitions.
- To validate persistent homology as a tool for analyzing complex systems.
Main Methods:
- Persistent homology analysis was employed.
- The mean-field XY model and the \(\phi^{4}\) lattice model were studied.
- Dynamically sampled submanifolds of configuration space were analyzed.
Main Results:
- Persistent homology analysis successfully identified phase transitions in both models.
- The method accurately retrieved the known relationship between phase transitions and topological properties.
- Topological features of configuration space submanifolds were clearly characterized.
Conclusions:
- Persistent homology is an effective computational method for studying phase transitions.
- The technique accurately reflects the underlying topological structures related to critical phenomena.
- This approach offers a novel perspective in analyzing complex physical systems.
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