Interpretable Phase Detection and Classification with Persistent Homology
arXiv:2012.00783
Abstract
We apply persistent homology to the task of discovering and characterizing phase transitions, using lattice spin models from statistical physics for working examples. Persistence images provide a useful representation of the homological data for conducting statistical tasks. To identify the phase transitions, a simple logistic regression on these images is sufficient for the models we consider, and interpretable order parameters are then read from the weights of the regression. Magnetization, frustration and vortex-antivortex structure are identified as relevant features for characterizing phase transitions.
5 pages, 3 figures; shortened version of arXiv:2009.14231; accepted to NeurIPS 2020 Workshop on Topological Data Analysis and Beyond