Persistent homology analysis of phase transitions.
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.
Aix-Marseille University, CNRS Centre de Physique Théorique UMR 7332, Campus de Luminy, Case 907, 13288 Marseille Cedex 09, France.
Irene
I
Donato
Aix-Marseille University, CNRS Centre de Physique Théorique UMR 7332, Campus de Luminy, Case 907, 13288 Marseille Cedex 09, France.
Matteo
M
Gori
Aix-Marseille University, CNRS Centre de Physique Théorique UMR 7332, Campus de Luminy, Case 907, 13288 Marseille Cedex 09, France.
Marco
M
Pettini
ISI Foundation, Turin, Italy.
Giovanni
G
Petri
NaXys, Département de Mathématique, Université de Namur, 8 repart de la Vierge, 5000 Namur, Belgium.
Sarah
S
De Nigris
Qstar, Istituto Nazionale di Ottica, largo E. Fermi 6, 50125 Firenze, Italy.
Roberto
R
Franzosi
Dipartimento di Scienze Matematiche "G.L.Lagrange", Politecnico di Torino, C.so Duca degli Abruzzi 24, Italy and ISI Foundation, Turin, Italy.
Francesco
F
Vaccarino