How much of persistent homology is topology? A quantitative decomposition for spin model phase transitions
Point-cloud persistent homology (PH) -- computing alpha or Rips complexes on spin-position point clouds -- has been widely applied to detect phase transitions in classical spin models since Donato et al. (2016), with subsequent studies attributing the detection to the topological content of the persistence diagram. We ask a simple question that has not been posed: what fraction of the PH signal is genuinely topological? We introduce f_topo, a quantitative decomposition that separates the density-driven and topological contributions to any PH statistic by comparing real spin configurations against density-matched shuffled null models. Across the 2D Ising model (system sizes L = 16-128, ten...
| Authors | Matthew Loftus |
|---|---|
| Primary category | cond-mat.stat-mech |
| Published | 30 March 2026 |
| Last updated at source | 30 March 2026 |
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