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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