Persistent Homology analysis of Phase Transitions
Statistical Mechanics
2016-06-22 v1
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.
Cite
@article{arxiv.1601.03641,
title = {Persistent Homology analysis of Phase Transitions},
author = {Irene Donato and Matteo Gori and Marco Pettini and Giovanni Petri and Sarah De Nigris and Roberto Franzosi and Francesco Vaccarino},
journal= {arXiv preprint arXiv:1601.03641},
year = {2016}
}
Comments
10 pages; 10 figures