Interpretable Phase Detection and Classification with Persistent Homology

TL;DR

This paper introduces a method using persistent homology and logistic regression to detect and interpret phase transitions in lattice spin models, identifying key physical features as order parameters.

Contribution

It presents a novel approach combining persistent homology with simple classifiers to discover and interpret phase transitions in statistical physics models.

Findings

Persistence images effectively represent homological data.

Logistic regression accurately detects phase transitions.

Physical features like magnetization and vortex structures are identified as key indicators.

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.