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 University, CNRS Centre de Physique Theorique UMR 7332, Campus de Luminy, Case 907, 13288 Marseille Cedex 09, France; ISI Foundation, Turin, Italy; NaXys, Departement de Mathematique, Universite de Namur, 8 repart de la Vierge, 5000 Namur, Belgium; Qstar, Istituto Nazionale di Ottica, largo E. Fermi 6, 50125 Firenze, Italy; Dipartimento di Scienze Matematiche “G.L.Lagrange”, Politecnico di Torino, Duca degli Abruzzi 24, 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.


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: 56
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