Persistent homology is used on Monte-Carlo simulation of lattice spin models. Phase transitions, order parameters and critical exponents are extracted from persistence images for two-dimensional models. Straightforward interpretability allows for features such as magnetization, frustration and vortex-antivortex structure to be easily identified.
See the following for more details:
A. Cole, G. J. Loges and G. Shiu, Quantitative and interpretable order parameters for phase transitions from persistent homology, Phys. Rev. B 104 (2021) 104426 [arXiv:2009.14231].