Quantitative and interpretable order parameters for phase transitions from persistent homology

We apply modern methods in computational topology to the task of discovering and characterizing phase transitions. As illustrations, we our method four two-dimensional lattice spin models: Ising, square ice, XY, fully-frustrated XY models. In particular, use persistent homology, which computes births deaths individual topological features as a coarse-graining scale or sublevel threshold is increased, summarize multiscale high-point correlations configuration. employ vector representations this information called persistence images formulate perform statistical distinguishing phases. For models consider, simple logistic regression on these sufficient identify transition. Interpretable order parameters are then read from weights regression. This suffices magnetization, frustration, vortex-antivortex structure relevant for transitions also define "persistence" critical exponents study how they related those usually considered.