Interpretable Phase Detection and Classification with Persistent Homology

Alex Cole; Gregory J. Loges; Gary Shiu

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arXiv · 2012.00783

Interpretable Phase Detection and Classification with Persistent Homology

Alex Cole·Gregory J. Loges·Gary Shiu

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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.

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cond-mat.stat-mech cs.LG math.AT

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Alex Cole, Gregory J. Loges, Gary Shiu. 2020-12-01. Interpretable Phase Detection and Classification with Persistent Homology. https://arxiv.org/abs/2012.00783

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