Interpretable Phase Detection and Classification with Persistent Homology
This work provides an interpretable method for physicists to identify and characterize phase transitions in statistical physics models, offering a new perspective on order parameters.
This paper applies persistent homology to detect and characterize phase transitions in lattice spin models, using persistence images as a representation. A logistic regression on these images successfully identifies phase transitions, and interpretable order parameters like magnetization, frustration, and vortex-antivortex structure are extracted from the regression weights.
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.