Persistent Homology analysis of Phase Transitions

TL;DR

This paper demonstrates that persistent homology, a computational topology method, can effectively identify phase transitions in physical models by analyzing the topological features of configuration space.

Contribution

It applies persistent homology to two physical models, showing it can recover known topological signatures of phase transitions from sampled data.

Findings

Persistent homology detects topological changes at phase transitions.

The method accurately retrieves known topological properties of models.

Analysis confirms the relationship between topology and phase behavior.

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.