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 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. 
Irene Donato, Matteo Gori, Marco Pettini, Giovanni Petri, Sarah De   Nigris, Roberto Franzosi, Francesco Vaccarino
cond-mat.stat-mech