  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.
