# Quantitative and interpretable order parameters for phase transitions from persistent homology

@article{Cole2021QuantitativeAI, title={Quantitative and interpretable order parameters for phase transitions from persistent homology}, author={Alex Cole and Gregory J. Loges and Gary Shiu}, journal={Physical Review B}, year={2021} }

We apply modern methods in computational topology to the task of discovering and characterizing phase transitions. As illustrations, we apply our method to four two-dimensional lattice spin models: the Ising, square ice, XY, and fully-frustrated XY models. In particular, we use persistent homology, which computes the births and deaths of individual topological features as a coarse-graining scale or sublevel threshold is increased, to summarize multiscale and high-point correlations in a spin…

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## 12 Citations

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