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Interpretable Phase Detection and Classification with Persistent Homology (2012.00783v1)
Published 1 Dec 2020 in cond-mat.stat-mech, cs.LG, and math.AT
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.