Persistent Homology analysis of Phase Transitions

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 XY-mean field model and by the phi^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.

10 pages; 10 figures

References in corpus (2)

• Statistical mechanics and dynamics of solvable models with long-range interactions
• Phase transitions and topology changes in configuration space

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