Persistent homology analysis of phase transitions.
basic_science · Level V
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- Record sourced from PubMed, PMID 27300860.
- Also identified by DOI 10.1103/PhysRevE.93.052138.
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Abstract
Persistent homology analysis, a recently developed computational method in algebraic topology, is applied to the study of the phase transitions undergone by the so-called mean-field XY model and by the ϕ^{4} lattice model, respectively. For both models the relationship between phase transitions and the topological properties of certain submanifolds of configuration space are exactly known. It turns out that these a priori known facts are clearly retrieved by persistent homology analysis of dynamically sampled submanifolds of configuration space.