Persistent homology analysis of phase transitions

Year: 2016

Authors: Donato I., Gori M., Pettini M., Petri G., De Nigris S., Franzosi R., Vaccarino F.

Autors Affiliation: Aix Marseille Univ, CNRS, UMR 7332, Ctr Phys Theor, Campus Luminy,Case 907, F-13288 Marseille 09, France; ISI Fdn, Turin, Italy; Univ Namur, Dept Math, NaXys, 8 Repart Vierge, B-5000 Namur, Belgium; Ist Nazl Ottica, Qstar, Largo E Fermi 6, I-50125 Florence, Italy; Politecn Torino, Dipartimento Sci Matemat GL Lagrange, Cso Duca Abruzzi 24, I-10129 Turin, Italy.

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 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.

Journal/Review: PHYSICAL REVIEW E

Volume: 93 (5)      Pages from: 052138-1  to: 052138-10

More Information: This work was supported by the Seventh Framework Programme for Research of the European Commission under FET-Open grant TOPDRIM (Grant No. FP7-ICT-318121).
KeyWords: Algebra; Wave functions, Algebraic topology; Configuration space; Lattice modeling; Mean field; Persistent homology; Submanifolds; Topological properties, Topology
DOI: 10.1103/PhysRevE.93.052138

Citations: 59
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